I'm Sudanarski. I'm co-director of the Education Policy Initiative at the Gerald R. Ford School of Public Policy. Nice to see you all here today. So this policy talk lecture marks the opening of the conference on student loans, which would not have been possible without the generous support of our co-sponsors. And I'd like to recognize the UPJOT Institute and the Spencer Foundation for their work and their funds in making this event happen. So thanks so much. So this conference is going to be bringing together some of the countries. I didn't write this. Some of the country's top minds on an issue that not only interests us, but affects many of us in the room. So today's speaker is President Obama's Special Assistant for Education Policy, Roberta Rodriguez. The most important thing to know about Roberta Rodriguez is that this is Wolverine. So he's an alumnus of the University of Michigan. He also got a degree from Harvard in education. But that's OK. Since then, he's been a disappointment. He was Chief Education Counsel with the late Senator Ted Kennedy, assisting in the development of education legislation. He contributed to the development of the No Child Left Behind Act. And he's worked on various reauthorizations of federal legislation, including the Elementary and Secondary Education Act, the Individuals with Disabilities Education Act, Head Start, Child Care, Higher Education, and the America Compete Act. And he'll tell you what that acronym means. So before I ask Roberta to the podium, I want to remind you that you've got a question for him, write it on one of the cards that's getting passed out of the entrance, or you can tweet it in using the hashtag policy talks, one word. And Roberta, the floor is yours. Thank you. Hi, good afternoon, everyone. It's a real honor to be with you here today for this important conversation. I really want to begin by thanking Sue and Dean Collins and the entire faculty here at the Ford School for inviting me to be here. And of course, special thanks to the Upjohn Institute and to the Spencer Foundation for their generous support of engaging in this really important topic. It's really great to be back home. It's really great to be back among my fellow Wolverines and here at our University of Michigan community to have the conversation here today. I really want to begin by making the connection that's rather obvious to most of us that are gathered here today, but I think it's nevertheless central to the conference and to the arc of the papers and discussions that you'll explore in the coming two days. And this is really the simple reminder that perhaps more than at any other time in our nation's history, higher education is really the engine for our economy and the spark that is going to continue to ignite our democracy. There are countless examples from across the country of how earning a college degree really opens the doors of opportunity for families, places them on a greater pathway toward economic mobility and prosperity and success. Examples of how the pursuit of a college degree helped young people find their place in their communities, in their worlds around them and in their country. And that was certainly the case for me during my time here at the University of Michigan in the mid-90s as an undergraduate that was still feeling his way about his academic path, eager to set forth and to change the world. And in today's economy, as President Obama reminds us, a college degree is the surest rung on the ladder of opportunity into the middle class. A new global economy brings new challenges, new demands, but it's very clear that gone is that economy of a quarter century ago, where a worker with a high school credential could make at least half of what a college graduate would earn across their lifetime. So we know that education is the strategy for our 21st century economy. Our children are competing with the rest of the world for jobs of the future and our long-term economic security is directly tied to the quality of the public education that we can provide today. That's why this topic that we're exploring over the course of this conference is so important. Many of you here are esteemed in this field in this academic discipline. You're familiar with the statistics. You know that our economy clearly rewards those with a higher education. We know that our college graduates have higher earnings that we know also that there's a real imperative here is eight and 10 new jobs in the U.S. will require some post-secondary education or training and the 30 of the 30 fastest growing jobs in our economy today, over half of those require a four-year degree. But beyond this economic imperative, we also have to, at the onset here of our conversations, remind ourselves of the moral imperative that we have, the moral responsibility we have in that we're a nation that defines ourselves based on our ability to provide every individual the opportunity to rise as far as their hard work and their initiative will take them. And so increasing access to higher education is fundamental to living up to that moral commitment. And it's one of the best things that we can do for our country. This is why we've organized our efforts in Washington around the goal that the president laid out when he first arrived at the White House. And this is a goal to lead the world with the highest proportion of college graduates by 2020. Our secretary of education, Arnie Duncan, he calls this goal our North Star. And that's exactly what it is. It's a guidepost and it's a reminder to us to strengthen education at every level and to deliver on this challenge. So in order to reach this goal, we'll need to increase the share of college graduates that we produce in our nation by 50% over what we've produced in 2009. And by the numbers, this means eight million more young adults will need to earn associates and bachelor's degrees by the end of this decade. We'll have to outpace our current rate of degree attainment relative to our population growth, which has us more or less producing about three million more college graduates by the end of the decade. So we've placed such an emphasis on this 2020 goal because we know that higher education is such an important investment worth making. We know, again, the median earnings of bachelor's degree recipients are markedly higher, $21,000 more than high school graduates. And we know that it really does provide a true ladder into the middle class of adults who grow up in the middle class, 31% of those that have a college degree were upwardly mobile into the top income quintile between 2000 and 2008. This is compared with just about 12% of those that did not have a college degree. Especially for students that are graduating into weak economies, it frequently and can often take time to find the path that ensures that going to college was really worth it. But those with more education tend to experience larger increases in their earnings as they age. And we know that based on current earnings patterns that if people with bachelor's degrees work full time over their work lives, they'll earn about two thirds more on average than our high school graduates. So we know we have this imperative that as a backdrop to this 2020 goal, it's an ambitious goal. The pace of progress for our young Americans in college attainment is very ambitious under this charge. But one thing is really clear. We're not going to meet it unless we really embrace a spirit of change in our higher education system. And that is going to involve a shared responsibility that spans from leadership at our higher education institutions to state legislators and governors, to public and private stakeholders, parents, and of course ultimately students to be able to accelerate toward this 2020 challenge. Reaching the goal will require also a collective will on the part of policy makers and partners, higher education leaders, philanthropy, others to really ask the tough questions that are ultimately going to foster change in our higher education system. Are we doing right by our students? Do they have the reliable sources of aid and support that they need to be successful and as they pursue their degree? Do our colleges and universities have the proper capacity to harness innovation? And are we equipped with the right incentives to drive reform focused on improving the educational experience for students while they're on campus? Are our federal and state policies well attuned with a mission, a vision, and a focus that promotes not only higher education access, but college completion? Are we confronting the state of teaching and learning on our college campuses and aligning it with the needs and demands of 21st century learners? Are we prepared to assume the collective responsibility to address the inequities that we have in college attainment? The college completion gap that still manifests itself on the basis of socioeconomic status and racial lines and ultimately is a serious threat to our economic standing in the world. We still have only about 30% of our young African-American students today and 20% of our young Latino population today that holds an associate's degree or higher. And then of course, one of the key questions that's posed most relevant to this convening today, are we prepared to do what's needed to tackle college affordability as a national imperative? America's home to the best colleges and universities in the world. And yet too many Americans for a variety of reasons feel like pursuing a post-secondary degree or certificate might be out of reach for them. Some are clearly hindered by the shortcomings that we have in our K-12 education system. There's no question that we need to do better to measure up to the challenges of graduating each and every one of our young people prepared for college in a successful career. But for many others, there is still this belief that college costs can be prohibitive. And whatever the reason, a person's decision not to go to college, not to pursue that higher education can have a direct impact on his or her long-term economic future and on the collective prosperity of our communities and of our country. So for these reasons, our administration has been really clear in our focus. We wanna help more students prepare for and succeed in higher education with a blueprint that is going to dramatically expand educational opportunity beginning in these early years, make the needed changes we need in our K-12 education system and commit to putting an affordable, high-quality higher education degree within the reach of every American. Now this issue of paying for college is something that more than likely has affected everyone here in this room. And I know while we are here to study this topic in greater depth, we also know that it's an issue that affects us personally, individually. I know for me the cost of college, the affordability of my degree, along with the stellar education, of course, that Michigan stood to provide me, was a really important factor in the decision in terms of why I chose this school for my undergraduate studies. But the fact of the matter is, while many Americans across the country understand why a post-secondary degree is so valuable, many folks still don't have access to higher education for one big reason. And that is that too many of our families still feel priced out. Now I know you'll hear plenty over the course of this conference on trends in student loan debt for completers and for non-completers across our country. We're really fortunate to have wonderful data just released this week by the college board and I believe Sandy Baum will kick off your day tomorrow with an overview of this new data that really provides the most comprehensive analysis of where we are with respect to our trends in pricing and in cost. But it's worth noting that at least one trend has remained constant as we look over the course of this data and that's that net price has continued to tick up across our institutions and the growth has come at a time when family income has not recovered from the economic downturn. So as the president has stated several times on the bus tour that he took just over the summer in the Northeast, he said family incomes are just not growing fast enough relative to the price of college. Tuition and fees at our public four-year colleges is now more than three times higher than it was 30 years ago. And while over this same period income has only risen 16% for middle-class families. So this has real implications on a family's decision about whether or not to pursue higher education. All across the country families are asking themselves this question around college costs. We hear it, we get these questions and we get these letters from families across America at the White House every day. And I think the administration has a lot to be proud of in terms of the amount of grenade and tax benefits and the progress that we've made to try to make sure that we have more of a reliable and affordable source of aid for families to be able to pursue college. I think as the data that you'll see that Sandy will present shows, in many places, the uptick in Pell, the uptick in some of the other grant aid that we've provided has been a enabler for net prices to not jump higher than they have. And in many venues, the bang that we get for our federal student aid is quite high. You know, at our community colleges, in many instances it covers full freight for tuition and fees with room to spare for other expenses in a student's budget. So we have set forth to eliminate wasteful subsidies in our higher education student aid system, subsidies that were funding banks to the tunes of $68 billion over 10 years, and to be able to recapture and reinvest those dollars, over $60 billion of those dollars in college access. We've increased the maximum Pell grant for working in for middle class families by more than $900. That's now reaching over 9.5 million families. We've created the American Opportunity Tax Credit, which provides a maximum of $2,500 per year and tax credits for college. And it's helping more than 11 million families defray the cost of college annually. You know, we've simplified the FAFSA. We've taken initial steps to have a shorter form and better online format and a skip logic that imports tax information for individuals who are completing the FAFSA and for their families. And studies show that if we do even more along this front, we can really boost college enrollment rates. And we've worked to invest in college access grant programs to help be partners with states in increasing the number of low income students who are prepared to enter and to succeed in college and to manage their debt. But for a majority of students who borrow in order to attend school, the increased price at four year colleges can still be a significant burden. And it's coupled with a really important factor here, which is cost shifting as states slash higher education budgets. As we see those budgets go down, families are being asked to shoulder the increasing cost of attendance and the increasing sums that are needed to finance their child's higher education. You know, all told, looking at data from the college board and from Tikus, the average student loan borrower now graduates with over $26,000 in debt. Loan default rates are rising at some institutions and as we'll discuss over the course of this conference, many young adults are burdened with that debt as they graduate college and begin the next chapter in their lives. This debt also undoubtedly has some level of ripple effect across our economy. So the fact that prices have continued to grow is causing some families to beg this fundamental question around, can I afford this? Can I afford college? I know we fundamentally all believe that students can and we are continuing to try to deliver that message. But despite the statistics that prove what a great investment college makes, what a strong return of investment that has later in life, the answer may not be so transparent to students and to families who are evaluating their options and assessing whether or not at this moment in their lives, perhaps, they can handle taking on the cost of college. So when the president takes to the road and has a conversation with the country around college costs, at the heart of this message that he delivered this summer was a value proposition. It was making sure that higher education, what we know as a central pillar to achieving the American dream is available for our students at a high quality, at an affordable price and with a reasonable expectation that it will prepare them for success after they graduate. So at the heart of this new national conversation on college affordability is this value proposition and we can't make significant headway in reshaping higher education to serve all students without placing this equation of quality, of affordability and of outcomes front and center. You know, each year, our federal government invests over $150 billion in student financial aid. At least two thirds of our undergraduates receive some type of credit to support their education, their higher education from the federal government and collectively states are investing about $70 billion in public colleges and universities. But as you all know, almost all of the federal student aid that flows to colleges is given based on the number of students that enroll, choose to enroll in that school. And what's missing from the equation is an important factor which is a focus on outcomes. So in order to live up to their international acclaim, our colleges and universities have to explore new ideas to improve learning and outcomes for students in the spirit of providing the most affordable and highest quality education possible. It's in this very spirit that we have earned our reputation as a nation, that our colleges and universities have collectively earned their reputation as a leader in the world. And it's again that spirit that the president is seeking to harness to maximize our investment in resources and time and energy and in focus on higher education. Earlier this year, we put forth a series of reforms centered around this aim of demonstrating value in higher education. It's not good enough to simply enroll students without attending to persistence and completion. Our institutions should not be judged and thrive based on the amount of money they charge students. And if some institutions fail to prepare students to graduate and to succeed in the workforce, we are ultimately missing our mark. So what we need is to accelerate that innovation to help colleges focus on their fundamental mission, which is providing a great education at an affordable cost. So our administration will put forth a suite of legislative and executive actions and proposals, a few of which I'd like to discuss today that we hope will not only combat rising college costs but really encourage innovation and encourage improvement across our higher education sector. And through this increased focus on value, hopefully we'll achieve a scenario in which students can pursue high quality paths in post-secondary education that will not leave them unduly saddled with that. Throughout this push for reform, the president's very clear that our colleges and universities will be the actors that will lead the way with respect to this change. We're looking at our higher education sector not only to continue the great work that's already underway by many institutions, but also to spearhead greater adoption for the innovations that can really lead us toward a greater vision of value for students. It's only through partnership with institutions that a spirit of reform and change will really take hold and can really deliver a more affordable higher education for more Americans. Now, as I mentioned earlier, almost all federal student aid resources are allocated based on the number of students who enroll, not the number of degrees that are earned or what students learn. So at a time when our federal investment is at $150 billion for federal student aid, and at a time when state investment is actually diminishing relative to need, we must demand greater accountability for our funding. So the first piece of this plan that the president's put forward is to connect student aid to outcomes. We are aiming to in turn drive a better, more affordable education by developing and publishing a new rating system for students and families to make use of. We don't believe that we should be ranking schools based on how expensive they are or how much they spend on capital improvements or what other elite peer schools think, but instead on metrics that reflect real value for families and for students. Metrics that families themselves can understand. So right now we have private rankings, US News and World Report and others that put out each year rankings on academic prowess of colleges and universities. It encourages a lot of colleges and universities to focus on ways to sometimes actually raise costs for students. And the president stated clearly in August that he believes we should rate colleges based on opportunity. How are we helping students from all backgrounds and particularly our first generation and our disadvantaged students be successful? And how are we providing that information to students and parents? You know, we're gonna ask questions like how much debt does the average student leave with? How easy is it to pay that debt off? How many students graduate on time? How well do graduates do in the workforce? Because we believe these answers will ultimately help parents and students figure out how much of value a college truly offers. You know, and our ratings will also measure how successful colleges are at enrolling and graduating students who are on Pell grants. It will be our firm principle that our ratings have to be carefully designed to increase, not decrease the opportunities for higher education for students who face economic challenges. So this is gonna take time. This is not an easy proposition, but we think it can empower students and families to make good choices. And we will give any college the chance to show that it's making a serious and consistent commitment to improvement. So a college may not be where it needs to be right now based on value, but there will be the chance to get better. You know, we're gonna develop this rating system through extensive public input sessions across the country to gather inputs from parents, from students, from state leaders, from academia, from college presidents and others. And we're gonna focus on measures such as access, affordability and outcomes. These new ratings will also ensure that colleges are doing their very best to encourage our neediest students to be successful. And the president has charged us with preparing this new system by the 2015-16 academic year. But we're looking forward even beyond that, and we hope to use this rating system in a much bigger way by calling on Congress to examine this proposition of value and of ratings as it allocates federal financial aid. Under this proposal, students will still be able to choose the schools that they want. I wanna make that clear. But we are proposing a proposition where taxpayer dollars will proportionally go greater towards schools that we know are working the hardest to deliver on this promise of affordability and value and quality. And in addition, we wanna make sure that more states are following in the footsteps of some of the leading states that are looking at performance based funding and performance based reforms and outcomes. States like Ohio, like Indiana, like Tennessee, that are doing great work to move their state higher education systems forward, and to focus on attainment and completion alongside enrollment and how they support their state public colleges and universities. By making competitive funding available, our administration is seeking to spur state higher education reform and reshape the federal state partnership by also encouraging that states maintain their funding for public higher education. This race to the top competition, this is something that was part of our administration's plans last year for higher education and included again in the president's call this August, will be squarely focused on what we can do to support greater access and affordability, particularly at our public colleges and universities, where about three quarters of America's undergraduate students are currently enrolled. Now, if we're gonna lead the world in the proportion of college graduates, we also need to be sure we are on the cutting edge of innovation on our college campuses. We need American higher education to do more, to really focus on teaching and learning and on reshaping that college experience for our students. The good news is we know that there are new and often better ways of pursuing teaching and learning at our higher education institutions. We don't need to look far to find examples of innovation and of pioneers that are looking at new developments and harnessing the power of innovation to lead higher education really toward a new frontier. We've seen examples from across the country. We've seen competency-based learning being tried now, not just online, but at colleges and universities across the country, including colleges like Southern New Hampshire University and the University of Wisconsin system that are doing more to realign and recalibrate their system to actually reward students based on what they learn, not how much time they spend in their lecture hall or in their seat. Redesigned courses that integrate online platforms are exciting new ways to bring technology in a blended fashion into teaching and learning in our college classrooms. You know, this National Center for Academic Transformation has shown the effectiveness of thoughtful use of technology across a wide range of academic disciplines, improving outcomes for students and reducing costs by nearly 40% on average. And e-advising tools, online learning communities, special cohorts of students, are encouraging persistence and alerting our college faculty when students need additional help to be able to be successful. You know, colleges can also award prior learning credit and experience for dual enrollment and for opportunities and learning that individuals, both young adults as well as adults, bring as they enroll in college and give them real credit for that toward their degree. So this rising tide of innovation has the potential to shake up our higher education landscape. You know, we still have a lot of approaches that are under development and too few students are actually reaping the benefits of this innovation today, but we have a proposal to do more to support a new first in the world fund that will test, evaluate and help scale innovative approaches to higher education that we hope will lead dramatically better outcomes for students and to make sure that we are developing and recognizing the leadership across America's higher education institutions to demonstrate that they are really truly helping their students learn in new and innovative ways. We're looking at new authority, regulatory and administrative authority to issue flexibility through an experimental sites authority that we have in the higher education act to promote high quality, low cost innovations in higher education and make sure that it's possible for instance for students to get financial aid based on how much they learn rather than the amount of time they spend in class. You know, we're looking at pilot opportunities to offer Pell grants to high school students who are taking college courses and allowing federal financial aid to be used to pay test fees when students are seeking early academic credit for prior learning or combining these traditional and competency-based courses into a single program of study. Another key component of promoting this value proposition in higher education is to provide new tools to help students and families understand their choices and the higher education landscape. You know, the new college rating system that I discussed here will help advance these efforts, but we've also made important and significant strides that we wanna make sure more American families are aware of to provide data to consumers in a clear and comprehensible way through two new tools that help students and parents understand what they're doing and why they choose and what their choices are in terms of a higher education investment. The first is a new Know Before You All campaign that includes a financial aid shopping sheet. And this shopping sheet is an individualized but standardized across the higher education sector, financial aid award letter that students and families get on the front end to understand the costs of college as well as what aid is available to them before making the final decision on where to enroll. The second is a new college scorecard. As many of you saw, this was released earlier this year as part of our State of the Union message. And the scorecard is designed to provide clear, concise information on cost, on graduation rate, on loan default rate, on the amount borrowed and on employment for every degree granting institution in the country. And we wanna make that scorecard available in an interactive, easy to read format for students and families to compare colleges and to make the best decisions for their future. We also have to make sure we're attending to the high default rates that we have in some of our sectors that we know are impacting the opportunity later for students to be successful and to repay their debt. You know, we have high default rates for instance in the for-profit sector where the highest average two and three year cohort default rates are at 13.6% and 21.8% respectively. Now here, our administration has tried to do more to make sure that we are bringing greater regulatory attention to bring greater accountability into this career college sector. Defining what it means for a program to prepare a student for gainful employment in a recognized occupation and to construct an accountability system that distinguishes between programs that prepare students for gainful employment and those that do not. So we're looking at new metrics for these institutions to measure their success and these regulations are aiming to support students in deciding where to pursue a post-secondary education by increasing the transparency of their costs and making sure that those institutions that are not delivering on gainful employment are not recipients of some of that $150 billion of our federal financial investment. Now, the other important element that we have to focus on here is also making sure that our borrowers have access to the tools and the resources that will help them to make responsible choices, responsible borrowing decisions and better management of their debt during repayment. So last year, we've looked at new loan counseling tools that are aimed at providing students with an interactive way to get the information they need at key points in their borrowing process. And as we continue to make improvements to those tools online based on feedback from our financial aid experts, our students and our families and our college counselors, we are seeking to do more to make sure that we are helping to support our borrowers at every point in their college experience. At entrance counseling, during school, and at exit counseling. We also have new options through the president's pay-as-you-earn plan, which started last year and enables many of our student loan borrowers to cap their student loan repayments at 10% of their income. And additionally, the administration's budget includes a new pay-as-you-earn plan that would expand that to all student borrowers who need it. Part of our challenge with pay-as-you-earn has been to make sure that we are targeting the subgroups of borrowers who are most likely to benefit and most likely to need this assistance. And so we are continuing to do more work in that area and implementing new streamlined applications for pay-as-you-earn as well as identifying some of our borrowers that might be at risk of default, those that might be in low-income households so that they know that they have opportunities to peg their student loan repayment to a manageable share of their discretionary income every month. So I hope you'll see the thrust of the reforms I've discussed here are really squarely aimed at demonstrating value in higher education. We know that some institutions at present are enabled to do better than others on this prospect. But it's our hope that with a new national conversation and a continued emphasis on outcomes, on quality, on affordability, we can collectively drive our American higher education sector toward the kind of results that will move our economy forward. Because we fiercely believe even with student indebtedness exceeding $26,000 on average, college is worth it. Just looking academically, we know we have plenty to support that claim, but there are thousands of individuals around the country who are able to attest to that. And we know we all have a role to play in this vision to again regain our standing internationally in terms of college completion. You all know well that the federal government can't take this issue on a loan or should it. We need partnership across sectors, across the nation to improve our system of higher education. We need states to do their part to prioritize higher education funding. States simply can't cut their higher education budgets to balance their broader budgets and expect institutions to just make up the difference or to pass along that difference to parents. We need states to do their part, we need colleges to do their part to act with creativity and urgency to contain costs. And they must hold themselves accountable for ensuring that students get an education that prepares them for success in the workplace. And we need our families and our students empowered with the information to make good decisions about where to attend college.  We know that our students will make decisions based on where value is highest so that they can spur the market into producing more of what's good. So ultimately all of this is in the broader vein of educating our way to a better economy and to a stronger middle class. That's what we're focused on as an administration. And we know that education is the surest path to get there. And a higher education is one of the single most important investments that we can make along that path. So thanks very much. I look forward to hearing your comments, your questions and your input for us as we move this agenda forward. Thank you very much once again for coming to speak with us. We have a whole bunch of questions. I hope you're ready. Yes. All right, let's start with this one. This is from the audience. Should we be concerned that linking college ratings to outcomes like graduation will provide incentives for schools to manipulate these measures? For example, by making classes easier or weakening college degree requirements? Yes, I think we have to be vigilant about that. This is, as I mentioned, is a challenging endeavor to develop a new rating system. And we have to be able to look at the interactive effect of the various variables that would be integrated there. There is clearly opportunity if we were looking at graduation rates, for instance, alone, to game that system. And that's why we also need to be looking at new measures around quality and making sure that we're focused and attending to the rigor of teaching and learning at our institutions. And we have some measures that we can look toward now there, particularly looking at gainful employment as one, but we need more. We actually honestly need more innovation in that space and we need better measures of teaching and learning at the post-secondary level. We have not turned our attention as a country from an education perspective to developing better measures there, unlike in our K-12 and early childhood sector where there are a lot of measures around quality. Roberto, my name is Mark Weederspawn. I am a doctoral student in the higher education program here at Michigan. This is kind of similar to the question that was just asked, but do you think that there would be any type of influence of this president's score on the current accreditation system? And if there's not, what do you think about the current accreditation system? Do you think there's any changes that we should be focusing on? Well, you know, I thank you for the question. I do think we need to endeavor to improve the current accreditation system. And, you know, part of the president's message at the beginning of this year in the State of the Union was to take on this challenge of reforming accreditation. You know, I think at the institution level, you have state level as well as regional and discipline-specific creditors constantly coming and looking at whether that institution's accredited. Many of those institutions, many of those processes do not focus on outcomes as much as they should. Many of them focus too much on inputs. So we believe we need to have a new conversation about accreditation. We're hoping we can have that as part of the reauthorization that Congress might consider of the Higher Education Act. And we also believe we need more alternate systems of accreditation because we believe that there are new innovations that are taking shape today in our higher education landscape that are not either well-suited or willing to go through the more traditional accreditation process, but that might be producing good outcomes for students. So we can't lose sight of that and we need an alternate process to be able to recognize that too. Thank you. Sorry, I neglected to introduce myself last time. I'm Dan Kreisman, I'm a postdoc here at the Ford School. I'm gonna give you one last one about the measures. What are the defining parameters of what the administration considers, quote, a high-quality education? For example, can you give us some more specifics of the factors that might go into the ratings? Sure, well, you know, we're looking at the rating system and at measuring issues like access. You know, what is the share of low-income, palatable students, for instance, that the institution is enrolling? We're looking at issues around affordability. What is the change in net price, for instance? And how does that square with, you know, some of the other data that we have with respect to maybe if it's a public institution, how much the state's investing in that institution? And we're looking at factors around outcomes. We're looking at default rates. And we wanna look at some measure of gainful employment, some measure of future earnings as an important proxy there. You know, right now, through the IPEDS process, the government collects data on about 15 different indicators across our higher education institutions. So we have quite a bit of data already out there. I think the challenge here for us is going to be how to distill that in a really thoughtful system that is fair to institutions that compares institutions in a fair manner, because our higher education sector is tremendously diverse. It's one of its strengths, right? We have great two-year colleges, great four-year colleges, public, private, career colleges, more liberal arts institutions. So we wanna be able to have a system that's gonna recognize the nuance there. And over time, we'll be setting forth a technical advisory group that will help our Department of Education navigate the development of this type of system. I guess we're gonna kind of switch gears a little bit here. This question's probably a three-hour, needs a three-hour response, but five minutes will do. Let's talk about gainful employment. Okay, let's talk about it. Yeah, can you just real quickly, where are we at on the state of gainful employment? How big of a factor is this going to be in the higher education system? And do you think that such a policy will possibly deter students from seeking out specific majors or philosophy? That is another three-hour lecture. We'll try to tackle it. You know, our administration has taken the first foray into regulating on the congressional requirement for gainful employment of career college programs. These are programs that are vocational in nature that are preparing students to enter a particular field of employment. You know, we have promulgated a rule earlier in our administration that looked at debt-to-earnings ratios as an important measure of success, as well as default rates in the context of calibrating a new system that looks at gainful employment and at whether individual programs not whole schools, but individual programs offered within schools are delivering on this commitment and this requirement by statute. Many of those schools are actually, many of those programs are operated at community colleges, but many of them are also operated at for-profit institutions and many of those for-profit institutions, some of them are wonderful actors, others, unfortunately, are not delivering or their, you know, students are graduating, unable to enter gainful employment or with very high levels of debt or default. So the key to making sure that we are not curtailing unnecessarily options for students is to make sure that we have a thoughtful system that's measured. I would point out that we're already beginning to collect data from the sector and I think we're seeing a relatively low share, less than modest share of institutions that actually are not able to meet the proposed metrics that were initially part of our administration's rule. But there are a number of institutions out there that have programs that didn't measure up. We now are back at the negotiating table, that's where we are right now because there was a part of our rule that was stayed by the court, by the circuit court and we are reconvening negotiators to look at redrafting a new rule around gainful employment. I can't talk too much about the particulars of that rule because those negotiations are actually ongoing into the next month and that regulation will continue to take shape. What I will say is we are gonna continue to pursue this because we believe that it's an important function of our government to be good stewards of taxpayer dollars. We do not want taxpayer dollars going to programs that are saddling students with debt and that are not resulting in gainful employment and not enabling them to repay that debt. And we are gonna take a close look at the concentration of programs that are failing those measures on the basis of the disciplines, right? Right now, I don't think we have data that suggests that there is a particular discipline that would be disproportionately impacted by the administration's original gainful employment rule but we'll continue to look at that moving forward because we now have, we'll soon have two years worth of data to be able to take a closer look at that question. I majored in philosophy. I'm not sure how much I would recommend that. So here's one from the Twitter world. If you could make one change in the entire education system to improve equity, I've had several questions about equity. What would that be? Well, that's, it's a challenge because there's a whole lot we need to do in equity across the pipeline from cradle through career. But I think the single most important change that can be made in terms of really tackling the impact of poverty on learning is to provide all of our children a high quality education before they reach kindergarten. And this, the contours of that plan as the president's proposed it is to provide preschool for all low and middle income four year olds in the country and make sure that that preschool is high quality. We have had study upon study that have demonstrated the return on investment upwards of $7 for every dollar invested. There's individual benefits. There are broader community benefits, economic benefits. And it's, you know, we've seen this also tried in communities around the country, both at the state level and at the local level. And we've seen tremendous impact here. I would turn folks to the recent study that was released by the Foundation on Child Development that Deborah Phillips, who was the author of one of the Neurons to Neighborhoods National Science Foundation studies helped compile that shows the benefits of high quality pre-K. We believe that it's one of the key drivers for equity moving forward. And if we can do that, we have the opportunity to begin to remediate that achievement gap and that learning gap that already is manifesting itself at 60 points between low income children and their more affluent peers by the time they reach kindergarten. This is another one from the Twitter, not the Twitter, from Twitter. There is no empirical evidence on effective loan counseling. So what is the Department of Ed doing to revise its services and why not fund research? Good idea. I think we should do more to fund more research on that front. You know, we do believe that we need to do a better job of reaching borrowers and providing them greater counseling. You know, we've definitely know that the tools that were provided previously were not sufficient. So what we've done is gone back to the drawing board and created a new interface that all students can interact on at, it's at www.ed.gov. If you link on student aid, you can interact with a college counseling tool and loan counseling tool that, as I mentioned in the remarks, really reaches borrowers at every point in their college career from entrance through school and then obviously exit counseling. You know, information and transparency around data is one of the most important things that we can do in this sector. In terms of providing greater focus on outcomes and on quality, in terms of making sure that families and students are well-equipped to make good decisions. And that's just something that we know to be true. I think we can probably fund research to better calibrate our loan counseling tools, but we don't, as a approach, see any harm in trying to provide students better and more targeted assistance and help in understanding the options available to them. To meet the president's goal for degree attainment, higher education must engage more non-traditional adult and part-time students. Federal policy seems to be shifting towards tying federal aid to shorter times to degree completion. How can these two imperatives be reconciled at the national policy level? That's a good question. You know, I think we have to acknowledge that four years is no longer a traditional trajectory for college attainment, right? I mean, I think we have that reality, you know, across our even traditional four-year public colleges and universities, that is certainly the case, if not more so, at our community colleges where you have, you know, and increasingly at our public four years, where we have more students that are working while they're pursuing their studies, more adults that are returning to pursue their studies and balancing work and family. And we know that we can't reach the president's charge to us around 2020 if we don't do more to help adults be successful in the system. So, you know, we have to keep that in mind as we're shaping policies and moving things forward. One example is to think about what we can do to support perhaps some changes or modifications to the PAL grant, particularly for adult students, right? And I think we've seen some innovative research coming out of Louisiana, you know, looking at performance-based awards for degree attainment that aren't necessarily pegged to the specific timeframe, but where awards are allocated based on the amount of credit that that individual accrues almost as a reward and for support as they pursue their studies, increasing and focusing on persistence. You know, I also think there are other interventions, smaller learning communities and cohorts of students moving through together, particularly for our adult students and our non-traditional students, so to speak, that research is found to be successful. So I think we need a myriad strategies there to be able to support our adult students and certainly we don't wanna have one-size-fits-all policy when it comes to making sure that our students are successful. We have to take into mind those populations. This one's gonna be, I think this might be from a professor. Because it deals with massive open online courses. They've kind of been viewed as a way to increase access at low costs. But how do we ensure quality? And what does the administration's role, or what does the administration think of the role of massive online courses in higher education? You know, we believe that technology can be a real driver for innovation in higher education. When it comes to massive online courses, massive open online courses or MOOCs, we believe that we have to do more to scale the types of assessments that are needed to know whether they work. You know, we don't yet have the series of performance-based assessments that enable us to know that as students are progressing through a particular online module or MOOC that they'll be successful. And so I think those assessments are currently being developed by a number of the various providers. We hope that, and we believe we have a role at the federal level to help support greater assessment and greater tools that can be used as institutions of higher education and private individuals develop these MOOCs so that we have a better sense of what's working in that space. I think we're still learning a great deal about what's working and what could work when it comes to online learning in higher education. Our National Science Foundation is doing some studies of that work as well. So we're gonna continue to learn from that. I'll say the one thing that I think is most exciting in this space is that once we're able to understand what adaptive platforms and what online innovations are most successful with our learners, we can apply that to the science of learning on college campuses. And if we can help support a new conversation with our faculty members about how to use technology and embed that in a blended way in their coursework, that has the potential to reach a far greater number of students that are currently enrolled and currently pursuing their higher education than just relying on MOOCs as a substitute platform for higher ed. Okay, there are two questions on this. I'm gonna amalgamate them here for you. And I'm also gonna paraphrase because one of them needs paraphrasing. So in essence, why create a rating system rather than just provide public information? The other one says, another no before you know campaign. Why is this administration so strongly focused on consumer choice? Well, I'll take the last one first, which is that we believe that the pursuit of higher education for too many students is too opaque. Honestly, we believe that we have not done enough to help support states in the process of defining standards and defining learning progressions that will help that are very clear, that are easy to understand for the public and that help particularly young people graduating from high school understand what it will take for them to get their college degree, understand the various pathways they have to reach a four year degree for instance. That's not to say that we're not seeing innovation in that space. We're starting to see states like Florida and other systems, the Arizona system for instance, that's starting to look at defining learning outcomes and aligning that articulation between two year and four year colleges so that students are actually able to more seamlessly finish their associate's degree, transfer to a four year institution and finish that and finish that four year degree in half the cost sometimes of students that might start out at that four year institution. So that's just one example of a place where we don't have enough transparency for families and for students.  We collect 15 different indicators. We don't provide that data in a really easy to understand, reliable format for parents or for families. So if you think about higher education as one of the most important investments you can make as a family, you're sitting around the college table or sitting around the kitchen table and thinking about choosing a college, you wanna be able to have that data just as you would if you were buying a home and you'd be able to go on home's database and be able to print out a comparable format to at least know it's not gonna tell you everything about those particular options but it at least provides a level of comparable data. We believe that's needed and that's why we're so focused on providing consumers information. Now, that's not all we need to do, right? That is not where this conversation needs to begin and end. We have a lot more to do to support affordability and innovation to actually make sure that translates into opportunity for students. I forgot the first part of your question, I'm so sorry. That's okay, I think that covered most of it. Okay. So Australia, New Zealand and the United Kingdom have income based loan repayment programs for all students. US limits this option to the lowest income borrowers. Why not expand this option for everyone? Well, I think it's a good question and a good issue for us to look at. We are focused right now on our low income borrowers because we have only a fraction of, we believe we have captured only a fraction of the students who most need and could most benefit from income based repayment. And that's why I mentioned we are starting to target some of our subsets of borrowers who we know might need the most help and could really benefit from IBR. But ultimately I think it's a good question and a good debate for us to have and something good for Congress to consider in terms of whether we can expand IBR more actively to more students and ultimately to all students across the country. We're not there yet, that's an expensive proposition as well. So it's something that we would really have to have the funding to be able to support. But it's something that we're eager to talk more about and to explore. So here's a question from Twitter about loan repayment. It says loan repayment is complex. Do you anticipate a partnership between the Department of Education and Treasury so repayment can go through the tax system? Yes, I mean I do think we are going to try to do more to support this. We are, we've been able to fortunately really forge a strong partnership on the income based repayment front as well as on the FAFSA front with our friends at Treasury to be able to import tax information in a more seamless way so that individuals are better able to know whether they qualify for benefits. You know, we think we should try to do more of that and try to do more of that experimentation with respect to loan repayment as well. And you know, I think we're not quite there yet, but you know, I think we're beginning to have conversations that haven't been had before between our Department of Education and the Department of Treasury to explore the possibilities there. This is from Twitter too. I think the first sentence is written in some sort of Twitter language. So if I read it. They're a lot of heads. Yeah. 21.8% cohort default rates in some for-profit schools. I don't know if that's a question or, but at what point do we shut them down or cut them out of federal aid? Yes. I mean, we believe we need to cut them out at some point of federal aid. You know, that is the whole premise behind the gainful employment regulation. And again, I can't speak to the details of that in terms of the thresholds. You know, we had a rule that we were very proud to promulgate as an administration on this. And you know, I think fortunately that rule would have not only had the effect of making sure that we were failing to provide the financial aid to the worst programs that clearly are bad actors of the sector. Because that level of default is just, you know, over 20% default rate. But it also I think potentially has the effect of the broader sector of career college programs improving their performance. And again, you know, federal regulation sometimes has this impact of if it's crafted in a thoughtful way of raising the bar and helping to improve the performance of other actors that may not be subject to the sanction. But that see that coming and know that there's a drive to get better and a need to do better. We believe that that's needed, particularly in this sector for the very issue that I mentioned in my remarks and that the default rates are so high. So on encouraging colleges to cut costs. So one way that colleges will cut costs is to increase the share of faculty or part-time low paid adjuncts. This seems likely to erode quality. How will the emphasis on affordability prevent colleges from cutting labor costs at the potential? So will this encouraging them to maybe hire more of part-time faculty, possibly erode teaching quality and have an adverse effect from what you're going for? Well, you know, I think this is similar to one of the earlier questions as well, which is that we need to keep our eye on quality here. And this can't be a trade-off in the name of affordability that compromises the quality of instruction or education at our institutions. And it's a challenge.  I mean, making sure that we have the right measures to know that our students are receiving a high quality education. You know, we have our outcome data post-graduation. That's the best and most reliable thing that we can look toward right now. But you know, we know that there are tremendous benefits to a great higher education, including the great liberal arts education that I received here. So, you know, we don't want to curtail that. And you know, we need to keep an eye on making sure that we have good labor practices across our education sector. That's something that this president is very focused on and very supportive of. Ideally, the percentage of low-income students attending college would and should be much higher than it currently is. However, how do you convince colleges from a business standpoint that creating programs to recruit these students is a good idea as low-income students would be bringing in less money to the school and they need more aid in the form of institutional grants and loans? That's a great question. You know, it gets to the premise of shared responsibility here. And it's not just around recruitment, it's actually around enrollment and completion. You know, because we have actually some really good recruitment programs and practices across our institutions, particularly in a number of our selective institutions, including the University of Michigan, does a fine job of recruiting our low-income students. You know, we also need to collectively share our best practice around making sure that we're retaining those students and that they are completing at our institutions of higher education. And that is another area where we wanna really invest in innovation and bring forth what's working well at our colleges and universities and help scale those types of practices at our institutions. But you know, ultimately we believe that we need to have real commitments here from our institutions of higher education to take those students, you know, we need to have a real honest conversation. And again, I'm not really advancing new policies in this space today in this conversation, but I do believe we need a national conversation around admissions, you know. We need a national conversation around retention. We need a discussion around those types of trade-offs around packaging aid. And you know, we have right now a situation where if an institution is well endowed and it has a real commitment to diversity, it has the ability and the will to be able to make more pathways available for more low-income students than other institutions sometimes do. You know, and then we have the question of public education for the public good and public higher education for the public good, which is something that I think, and I hope we as a country have a conversation about in this higher education reauthorization because the strength of our public colleges and universities is that it has to be able to serve all of our individuals and particularly be that pathway for our low-income and first-generation college goers to be successful. So, you know, I don't have a perfect answer for that, but you know, I think there's, it's a question of will, both political will of the institution, of its Board of Regents, of its leadership, of the state, and then also means to implement programs and practices, both recruitment and retention that are successful. I think we have time for one more. How is the administration looking at the, into the quality of K-12 preparation in terms of college success? So, you know, we have forged an ambitious agenda to really improve the quality of our elementary and secondary education system over the course of the first term. This is another lecture, which could be another couple of hours, but you know, ultimately we've really launched a new national effort to help support states in a new partnership around raising standards so that they actually prepare students for college and career level work. I don't think the public fully appreciates where we were with respect to college and career readiness as a system. We had standards that, you know, were defined by 50 states and curriculum, obviously that's defined by over 15,000 school boards. So we have a very disparate system, but we need, if we are to be successful in preparing our students for college, we need to begin with the expectation that they must graduate, each and every one of them college ready. And that's college ready at a level of learning that prepares them for entrance into a four year college without the need for remediation. So we had states that were setting standards, let's take seventh grade math, for instance, at levels that were 70 of mastery, levels of mastery, that were 70 points below neighboring states, right? That's over two grade levels worth of learning in terms of what's expected for students to be successful, just illustrative in middle school math. We are not gonna be competitive as a country if we are having that level of variation in that a student zip code determines the level of mastery at which he or she is expected to attain. So we have launched a race at the top and we've supported a new reform and redesign of the No Child Left Behind Act with new flexibility agreements with our states to be able to recalibrate these systems, these state systems to college and career readiness. And I think once we're able to really raise those expectations for all of our students so that they are competing in earnest with students across the globe, rather than learning at a level of mastery that is really substandard. Only then will we really be able to get where we need to go with respect to preparing all of our students for college. Let's totally have time for one more. Okay. Last one here. In our rating systems, we'd like long run measures like earnings because we think that the short run measures might not accurately reflect the quality of this school. It doesn't look like we will have those in our rating system when it starts. How will the system get around something like that? Well, you know, I think we're gonna need to look at the measures that are at our avail. I don't wanna predetermine what specific metrics will be in the system nor how they will interact because that is something that is still under development, careful development by our administration and it's something that we're gonna be seeking public comment on and advice from technical experts about. I will say that, you know, I think we need to look at as reliable data as we can find with respect to earnings and post-graduate outcomes. And we're hopeful that we will have some good long-term data to be able to look at. I don't know whether it's gonna be reliable and comparable across every institution, but we're gonna keep our eye on that and we're gonna look to the support and help of experts to figure out how that might be calibrated into a broader system. Thank you very much. Thank you. Thank you, Roberto.


We will from the next class try to see a method which will be very familiar to many of you, you have already done it. I mean from donkey's ears you have been solving these equations. So initially the kind of stuff we will be covering will seem very familiar to you particularly those of you who have done a preliminary course on linear algebra you might find the first few lectures are kind of repetitive. But it is hoped that as soon as we get into a more formal description of stuff you will begin to see the application of these ideas how they are abstracted out right. So we will no longer deal with just systems of equations that look like matrices and stuff. We will see that you will define generic objects like vector spaces ok. And when we deal with vector spaces we will see that the same ideas that we have learned for solving these linear systems of equations they can be just extended to problem domains that you might not have thought of. For example you can be dealing with spaces of functions and you can talk about how close is one function to another function right. These sort of ideas will come in when we describe things like norms. Speaking of which by the way I can also say there is another kind of algebra you might have already done without maybe knowing about it formally which is something called a Banach algebra. Anyone's heard of this? At least maybe some of you have heard of something called a Banach space. Remember what a Banach space is putting you through a lot ok no problems. So you see that when we learn linear algebra the notions that you acquire from this will help you in learning and also grasping the sense of other more sophisticated domains of mathematics. So this is like a stepping stone in that sense. So what is a Banach space? I will be using some terms please allow me to do that cut me some slack here. So when we talk about a Banach space right we have the following ideas in mind it is a normed vector space if that doesn't make sense at all welcome about this course. Normed is basically the abstract idea of a distance we shall see how it can be extended to arbitrary space vector spaces not just Euclidean spaces. So that's norm for you for the time being just keep that in mind. What is a vector space? Well that is a whole new kettle of fish altogether. I will not trivialize it by just wishing it away and saying oh you know it's this or that. We will go through a formal description of what a vector space is but that is why it is important to know linear algebra because then you will be able to appreciate what these things are. But here's one more notion that again you might have been familiar with earlier that is complete anyone knows what complete completeness implies. Let's just do this as an exercise in some mathematical terms and figuring things out okay. Don't think of this like some formal syllabus kind of thing that you're doing here. This will not be even discussed in this course okay but just you know it's good idea to just exercise our muscles a bit.  Have you heard of it? Yes. So that again brings us to the idea of what is a Cauchy sequence yeah. So what is a Cauchy sequence? It's after the name after the famous French mathematician Cauchy sequence. I'm sure you know what a sequence is right. Sequence I'm not going to define here right. It's just an arrangement of objects. Most cases you've encountered real numbers right. So Cauchy sequence is a very special kind of a sequence. What is it? So the way to look at these things these definitions is to look at them piecemeal term by term okay. I could already see some of you like you know throwing your hands up in the air and say oh here we go again with this Cauchy sequence and completeness and no tired of these jargons. Well irony is you are in the math department so yeah live with it. So this is a Cauchy sequence. What's the Cauchy sequence then? Here goes. Suppose you have this sequence some xk and heaven knows how many terms probably infinite but countably infinite terms Cauchy sequence. So suppose this is a sequence. So suppose is a sequence okay. If again we'll get into some domain that you may again think oh again come on but just bear with me a while. If for every positive epsilon okay epsilon, epsilon delta the continuity arguments you've heard again from time immemorial right. If for every positive epsilon there exists get used to the symbols. So maybe that's why it's a good exercise today right because we'll be using this in our proofs these symbols at least. There exists a natural number right n yeah. So this is a set of natural numbers. So some natural number begin in the set of natural numbers such that for all I'll just let you absorb those symbols slowly. For all m small m, small n greater than n the distance between which we denote by this xm minus xn is less than epsilon okay. That doesn't complete it. Then x is a Cauchy sequence seems a little familiar now. That's Cauchy sequence right. It's a Cauchy sequence or how to view this? I always try to view these things like a game of cards. So it's like two players playing one player throws in an epsilon yeah. If I have to trump that card I have to find my trump card in the form of n so that I can find a point in the sequence somewhere which is this big n to the right of which it doesn't matter which two terms I pick. This is very important. It's not two consecutive terms remember. It's not xm and mxm plus 1. It's not how the consecutive terms are varying. In fact you can actually take as an exercise a term like this okay. A sequence like this where you will see that each consecutive terms the difference gets small but this is not Cauchy. You can check. So the point is that no matter which two terms I pick to the right of this I can always fit them in to be closer and closer to each other. Closer than a certain predefined card that has been played or if you like football maybe this is the goalkeeper you are setting before the goal. If you set an M.E. Martin is you are setting a very small epsilon yeah. You wouldn't want to give me a goalkeeper who's incapable right. Then I can just play any shot blindfolded and probably it will go to the goal. Maybe not blindfolded but anyway in the right direction it will go for a goal. You want to set your best goalkeeper. What's the best goalkeeper for you? Give me a smaller and smaller epsilon to challenge me because if you allow me a large epsilon I'll have my job very easy right. I can always choose some number. It is only when you choose epsilon to be smaller and smaller that my job gets tougher. So your job is to throw the most challenging epsilon possible at me and if I am still able to spit out some N so that this is true then I prove that the sequence is cauchy and won the game. If not then you win the game it's not cauchy. That's the way to view this okay. That's the way to view these definitions. Don't think of them like some terms being thrown in stewed aside just for confusing people. It's there's enough clarity there that's very important. Now the point is is every cauchy sequence convergent. Convergent in what? That is the important thing. It seems like cauchy sequence is a very nice kind of a sequence that should converge. But the point is you look at a sequence like this 1 by N over the interval the open interval 0, 1 and you see that 0 and 1 are not part of this interval but this as limit N tends to infinity tends to 0. So this 0 is not part of this. So over this interval this sequence even though it's cauchy it doesn't converge. So therefore this is an example of a set that is not complete because by definition a complete space or complete you know if anything has a complete structure like the one we were talking about a while back this Banach space every cauchy sequence must have its limit over there inside of that set must be contained in that set. If it's not contained in it yeah if there are some cauchy sequences whose yeah which do not converge to points inside that you cook up cauchy sequences from elements in that set or elements in that space it's a space because it's got a norm it's got a structure. You cook up cauchy sequences from elements in that space and if those sequences do not converge to points inside that space then it's not a complete space. So in order for something to be a Banach space it has to be a normed vector space that is also complete so that every cauchy sequence converges to a point therein but that's just a definition. So we have the definition of a Banach space so fully of course we haven't cleared what is a Banach what is a vector space what is a norm those we will learn by the time you're done but why is this Banach space of importance because some of you have done some courses maybe on control theory or things like that you have actually dealt with Banach algebras which are defined on Banach spaces. So what is a typical Banach algebra just like we've seen a sigma algebra while back a Banach algebra is basically a Banach space. So b is a Banach space and you have a multiplication operation therein yeah so when I say a multiplication operation the way we describe it is this is not such that okay this takes objects two tuples or two objects from b and after this operation it spits out another object in b that's all that this symbol means okay don't read too much into it just try and understand this I'm just trying to give you a light introduction to some of the symbols and things that we shall be using okay what this means is that this is an operation that acts on two objects of this set at a time and spits out another object in that set in general it could be a set here it's a Banach space. So this multiplication operation when you define on a Banach space so of course in a Banach space there's already an addition that's sitting that addition operation is there now this multiplication operation satisfies the following property one there exists an identity of course in the Banach space such that I operated with f is equal to f for all f in the Banach space so there is an identity element in this Banach space. So in order for this Banach space in along with this multiplication operation to qualify as a Banach algebra okay these are the rule basis the first rule that you must have an identity element identified corresponding to that multiplication otherwise tomorrow you can call some operation a multiplication and give it your name and say oh this is a Banach algebra but I'll ask you to prove hang on what is the identity element with respect to this operation that you've named after yourself yeah and then you say oh this is the identity okay I'll say okay first check done what's the second check whatever multiplication operation that you have named after yourself in this supposed Banach space yeah must also satisfy the associativity property so for all g1 g2 g3 in that Banach space you must have g1 g2 g3 so this this denotes the multiplication operation is equal to g1 g2 g3 so basically the order of the operation it doesn't matter whether you do this to first and then this or whether you do this first followed by the concoction of the other two it doesn't matter that's the associativity property we will come across these associativity and all these properties very shortly in our course to in a different context but it's important to know the names this is tantamount to the existence of an identity this is tantamount to the associativity of the operation there is also another property there is also another property which is with respect to the scalars so for alpha is a scalar so suppose alpha is a scalar then for g1 g2 coming from the Banach space we have alpha acting on g1 subsequently acting on g2 is the same as alpha acting on g1 and g2 together so even this is some sort of associativity with respect to the operation of course this is not the multiplication operation because this is just a scalar multiplication we will make distinctions between the multiplication that we define and the multiplication that is already known which is the scalar multiplication it's very important to pay very close attention to these distinctions otherwise you lose the plot pretty soon okay remember this multiplication operation and this is not the same so this is a non-trivial assertion okay look this operation is the multiplication we have defined maybe I should use a different color perhaps so this is an operation that is pre-existing already that is already understood similarly this is an operation that is already understood it says that when you have this acting on this it's the same as you pull out the scalar get this operation done in terms of the new operation you have defined as you have defined and then do the known operation it doesn't matter still okay it's it's a non-trivial assertion it's not very obvious it's not you know something very similar in flavor to this because there are two operations that are going on here okay so this is the third property I presume there's a fourth property which is that because it's a normed space the Banach space so you have under your multiplication that you've defined again very important this is less than or equal to this is the submultiplicativity of the norm so again I reiterate this multiplication operation is different remember this operation is the one that you have just defined this M but this multiplication operation is between two scalars because the norm spits out a scalar right so this is non-trivial okay so this the identity there's the associativity there's a submultiplicativity of the norm there's this associativity with respect to the scalar and finally there's the distributivity with respect to addition so if you have g1 operating on g2 plus g3 you might just as well say that's the same as g1 acting on g2 plus g1 acting on g3 okay of course it is understood I'm not writing it that all of these are part of the Banach space g1 g2 g3 so on so any algebra any operation that you define on a Banach space any multiplication operation that you didn't define on a Banach space which means these conditions results in a Banach algebra and the moment you have a Banach algebra a lot of beautiful things happen one classic example of Banach algebra is for those of you again as I said who have done a course on control theory when you take transfer functions yeah this transfer functions this GSS not just the scalar ones I mean right you have matrices of transfer functions for multi-input multi-output systems those are Banach algebras okay so very very important idea in control theory this idea of Banach algebras right so you have done these algebras although we have not given them these monikers before right but from now onwards since we are doing a little more formal abstraction in this course we shall be delving into the names of these objects trying to understand the definitions clearly


update. And welcome to the 2pm update with David White at TFNN. Right now we're up on fairly light volume about three-quarters of a percent on the S&P. I'm looking for the latest volume here. See if we can't dig that up. But well if that's right 6.7 we must have picked up a lot in the last hour or even 15 minutes because we were fairly light through about one o'clock. And I haven't been watching it closely since then. Anyway up 1.16 percent on the NASDAQ Dow's up four tenths of a percent. Gold's up about a quarter. Crude's up three percent which is kind of the big mover. A lot of discussion from Crude and Energy of course in front of the OPEC plus meetings and discussions. So we'll see about that. Markets kind of pushed up on light volume. I suspect we'll have some fireworks tomorrow morning as we get econ news around 8.30 in the morning until then I think it's a lot of people making a lot of guesses. Of course today is options Delta neutral day. That is when option market makers get in the last eight trading days of monthly and sometimes 60 and 90 day options outstanding.  The idea is that they lock in whatever profits are there and are more than willing just to accept whatever the decay is in the options between now and then. So you know worst case they break even. Best case maybe they make a lot of money on the decay in the last eight days of the options. And it's kind of like a battery where you get the three year four year battery warranty and no matter what you get the last year of that and you get like $20 off of a hundred and fifty dollar battery or something. It's not much but they they protect that money fairly well. Anyway we'll have a lot more on that in the show in a few minutes. The reality is that navigating financial markets can be risky.


One thing I know is that art goes hand in hand with history. Art is a way of knowing how the heart speaks, how the mind functions, and how it expresses itself to the world. Art is a very valuable way that we know about the human experience. So without, if we really wanna tell the story of human history, if we really wanna know the facts about life, you have to include art. My name is Taz Elias, and I am the Brand Collaborations Lead in the Brand Studio of the Communications Department at the Wikimedia Foundation. This is a panel discussion with myself, Sherry Antoine and Inam Bosoka about the Unseen Project, a project that looks to highlight visual knowledge gaps amongst Black, Indigenous, and people of color. Let me introduce Sherry. Hi, how are you? I'm Sherry Antoine. I'm the Executive Director of Afro Crowd, an initiative focused on the African diaspora and the Wiki community. I'm also the Lead Organizer of a user group called Wiki Caribbean. And let me introduce Inam. Hi, I'm Inam Bosoka, and I am an illustrator and a sculptor from Ghana. I live and work in Accra, the capital city of Ghana. You know, we are all individuals, right? None of us are alike. We all have different fingerprints. We all have different spheres of influence. We all come from different places. And that includes people of African descent. And now while there are many different kinds of us, just in the three of us, we come from different places. We speak different languages even or around different kinds of folks and different influences. But all of us will likely be represented very similarly in a lot of the media that we see online. And so as a Black woman, who's also happens to be an immigrant in the country that I live, a lot of times, there are different ways that we are represented that aren't necessarily representative of us. And a lot of times we don't get to represent ourselves. Other people make those decisions for us. So one of the reasons that I'm so happy to be part of the Wiki community is that we get a chance to work on improving that, at least in this sphere online. But I know that we're much more complex than the two dimensions that we are often represented as. So visually, especially when that's missing and you're missing in the annals of your history, it can have a psychological toll. I am from Africa, obviously. And I can relate to what Sherry has said in a lot of ways in that we are currently the same people as certainly in different parts of the world. I think that Africa is not that much represented on the global or on the internet as you put it, right? There's no denying of the fact that much less is known about Africa globally. In my line of work, I often refer to the internet most of the times in search of inspiration and reference and maybe some things like that. And I often find out that there is not enough information about Africans out there. For example, I could be out there just looking for an African woman or an African lady. And on the first few pages, you may find pictures and a likeness of people from Africa. And then the pages that follow, you tend to find people that are not Africans and you start to wonder how come those are part of the particular word or phrases that you keep on which you were looking for. And so I think to, I can even say that Africa even lacks more in terms of what is out there about the people that are from here or the cultures and the things that happen down here in Africa. That means it's a great opportunity to connect with people like you. There are people all over the world doing such amazing things in different projects on Wikipedia. And I don't think, I think in the last five or six years, it's been more of an explosion of that. And so that's very exciting. And there's also been a push for greater representation. As you know, historically speaking, sorry, Wikipedia, which Wikimedia helps to run is 20 years old and for most of its history has been written mostly by Western Caucasian men. And I think it was like for a while there was either, it was above 80%, I think it was close to more than that. And over time, because of efforts to improve numbers like that with greater representation for example, of more women, people of color and so forth. Women for example, it's now, I think it was before the number of women represented on Wikipedia I think was in the teens. And now I think we've reached about 20%, which isn't perfect, but it's better than before. I understand you guys, Wikimedia, Wikipedia, you guys deal with information and putting knowledge out there so that it can be accessible to the whole world. Whilst you have done your research and have come out with the necessary information, I think that kind of helps illustrate those your points or whatever research you've come out with in a way that it helps people, people are able to relate to the stories that you make. People are able to, like I said, people are able to relate to the stories even more through acts. I mean, there is no doubt at itself in a form of, has served in a form of records in history books and so I think acts going hand in hand with history makes it important for an artist to be part of a privilege such as this one. So yeah, so I'm happy that I can also contribute my bit to the bigger goal or the bigger picture that is being created by Wikimedia. Before there was language that was written, there was artistic expression. I'm a violinist and music for me is the art, one of the arts that I love and I love that on Wikimedia, we can even add things like that. Art is a way of knowing how the heart speaks, how the mind functions and how it expresses itself to the world. Art is a very valuable way that we know about the human experience. So without, if we really wanna tell the story of human history, if we really wanna know the facts about life, you have to include art. And so that's a very important part of what we're doing here in this project to tell the story of the black experience of people of African descent all over the world, but also in general when we're doing anything related to data, I think it's important to consider that very important portion of our full human understanding. I am very excited, I have to say. Even though we are just at the beginning of the project, I've been new to get to know a lot more people from like you, like Sherry, and I guess there are a lot more that I am yet to meet. We're using data, we're turning that data into a representation that the world can see, right? But what's so great is that number one, they get to be seen because that's the whole point, right? These people are missing from the annals of our digital history, which is by and large becoming our history period. That's where people go to learn about the world around them in many ways about themselves. But what's wonderful is that these different artists are bringing their expression and we're translating it into what we see in front of us. And imagine all the ways that other people will be able to do the same thing. So in some way, what they're creating is a reflection, not only of where they're coming from, which is always gonna be that way because that's just human nature, but it's almost like looking in a mirror at ourselves for those of us, especially of African descent, but just people in the world to be able to see this expression and say, okay, this is who this person is. And now they're gonna take what they, their own understanding and perspective and then that becomes a lot more personal to them because of that. I think most importantly, it has to do with the fact that they are more of education. That is why I am much attracted to them. I feel education has a huge role to play as far as taking us to the next level as concerned. This is not the end of the project, that these, this is just the beginning, that there's more people who will be interested in continuing on the project and getting more faces that are not included to be included. I hope this project continues because there's just so many more possibilities. We want to include people from different backgrounds. It goes along with the problem, which is the black community or Africans and diaspora, not being represented enough online. And so at the end of the project, maybe it doesn't end, maybe it just goes on and goes into different forms. I guess it's going to provide a good enough information online and that is accessible to those who might be interested in it for academic consumption or people that might just be interested in knowing about certain things that are related to the people from Africa and then the diaspora. Please tell us a bit more about throw crowds. Can you describe our throw crowds mission in one sentence and then tell us a bit more about Afro crowd in general? Afro crowd's mission is to essentially highlight and involve the African diaspora on a comedian. So our mission is we're focused on the African diaspora and we're focused on not only engagement with the African diaspora, but also inclusion of it. So it's both front end and back end. So who's telling your story? Who's helping to write your history as a person of African descent? And also to ensure that you can be a part of that as well in this particular way, in the wiki community. We want to encourage people, regardless of whether you join us or some of the other groups online, regardless of your background actually, because we're open to anyone and everyone who's interested in participating with us of any background. What we also want to do is when you join Wikipedia as an editor, that you know that there is a supportive community there waiting to welcome you. And also through whom you can ask questions, you can try things out. And if we don't have the answer, we have a large community that we're connected to to help you get the answer.