Linear second-order equations; separation of variables, solution by series expansions. A concrete introduction to abstract algebra. At least one elective must be a Mathematics Department course numbered 3000 or above. PHONE: (315) 445 . We welcome everyone to join, whether you are a student, a postdoc researcher, or a faculty. /Producer (Apache FOP Version 2.1) Final: 35%. Select one of the following three courses. The course contains applications to life sciences, chemistry, and environmental life sciences. Mike Miller (College of Natural Science, '99) is a PhD Physicist and a leader in cloud computing, helping to bring cloud technologies to Fortune 500 enterprises. Learn more about Stack Overflow the company, and our products. The Volatility Smile. Multivariable calculus and linear algebra from a rigorous point of view. No a prior i background in the life sciences is assumed. This course is best suited for students who wish to focus on applications and practical approach to problem solving, rather than abstract mathematics and mathematical proofs. MATHUN1208HONORS MATHEMATICS B. Undergraduate Students Class of 2024 Applied Physics Juniors Another requirement for majors is participation in an undergraduate seminar, usually in the junior or senior year. Note that such students who decide to start with Calculus III may still need to take Calculus II since it isa requirement or prerequisitefor other courses. MATHGU4391INTRO TO QUANTUM MECHANICS. Programs, Institutional Program, Curriculum Covering spaces. Schedule, Preparatory "t a","H 2012. A theoretical introduction to analytic functions. Products of topological spaces. Plane curves, affine and projective varieties, singularities, normalization, Riemann surfaces, divisors, linear systems, Riemann-Roch theorem. Future, Premedical Elements of the calculus of variations and optimal control. Intended for students who are considering majoring in mathematics but wish additional training. Mathematics & Statistics for Financial Risk Management. Heisenberg uncertainty principle. Students with a score of 5 on the AP BC exam or 7 on the IB HL exam may begin with MATHUN1205 Accelerated Multivariable Calculus. The first half will reasonably closely followHatcher's notes on point-set topology, though if time permits we'll talk about some topics that he doesn't write about. Prerequisites: (MATHUN1101 and MATHUN1102 and MATHUN1201) and and MATHUN2010. Homework:There will be a total of ten homework assignments. Pages 5 Ratings 100% (1) 1 out of 1 people found this document helpful; Course Hero uses AI to attempt to automatically extract content from documents to surface to you and others so you can study better, e.g., in search results, to enrich docs . Aside from the courses offered by the Mathematics Department, cognate courses in areas such as astronomy, chemistry, physics, probability, logic, economics, and computer science can be used toward the major. Grading: The final course grade is weighted as:
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Other topics as time permits: elliptic functions, the gamma and zeta function, the Riemann mapping theorem, Riemann surfaces, Nevanlinna theory. Before starting his career in finance, Mr. Miller studied economics at the American University of Paris and the University of Oxford. Prerequisites: score of 550 on the mathematics portion of the SAT completed within the last year, or the appropriate grade on the General Studies Mathematics Placement Examination. "FV %H"Hr
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c0 L& 9cX& Development, Multicultural MATHGU4155Probability Theory. I will direct that most math questions you ask me be posted to the Discord, so that my response is a matter of the public record (instead of stuck on an email chain between the two of us, that nobody else gets to see.) Select the best result to find their address, phone number, relatives, and public records. Additional courses may be selected only with prior written approval from the Director of Undergraduate Studies. 3 points. Honors, Study The second term of this course may not be taken without the first. School, General Vari Hall500 El Camino RealSanta Clara, CA 95053(408) 554-4455. Story; . In order to be eligible for departmental honors, majors must write a senior thesis. Curriculum, Course Topics in abstract algebra used in cryptography and coding theory. 4.00 points. The major in mathematics is an introduction to some of the highlights of the development of theoretical mathematics over the past four hundred years from a modern perspective. . Students can receive credit for only one calculus sequence. Final: Tentatively, December 17. References for the second half will be more scattered. Financial Aid, University Upon completion of this course with a grade of C or higher, they may receive 6 points of AP credit. If you want additional references for your personal use,Munkres' bookis usually the standard reference, and quite comprehensive; some additional topics in the first half that aren't covered in Hatcher will certainly be covered here. Michael B. Miller is the CEO of Northstar Risk Corp., a risk management software and consulting firm based in New York City. While Calculus II is no longer a prerequisite for Calculus III, students are strongly urged to take it before taking Calculus III. The selected course may not count as an elective. D'hyacinthe et d'or; \ MATHUN3952Undergraduate Seminars in Mathematics II. Prerequisite: three terms of calculus and linear algebra or four terms of calculus. Differential forms and Stokes' theorem. 2019. Note that Calculus II is a prerequisite for Accelerated Multivariable Calculus, and both Calculus II and Calculus III are prerequisites for Calculus IV. } 4(JR!$AkRf[(t
Bw!hz#0 )l`/8p.7p|O~ The Instructor section of the form has already been completed and does not need to be signed by the professor. Mike's path to venture capital was atypical. Algebraic number fields, unique factorization of ideals in the ring of algebraic integers in the field into prime ideals. Email: smm2344@columbia.edu
Clinical and Research Opportunities, Premedical homework will also be posted to Courseworks
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{{{;}#q8?\. Groups, homomorphisms, rings, ideals, fields, polynomials, field extensions, Galois theory. Michael B. Miller is the CEO of Northstar Risk Corp., a risk management software and consulting firm based in New York City. Quotient spaces. The second term of this course may not be taken without the first. The purpose of this association is to support and increase the visibility of its members: individuals of historically marginalized minorities in APAM, including but not limited to women. Before that he was the Chief Risk Officer for Tremblant Capital, and before that the Head of Quantitative Risk Management at Fortress Investment Group. What motivated Rademacher's contour along the Ford circles? Through a strange twist of fate, Miller then co-founded Silicon Valleys most active seed-stage venture capital firm with Joe Montana and Michael Ma. A 2007 graduate of Mount St. Marys University with a bachelors degree in Communications Studies, he went on to earn a Masters of Business Administration in International Business from Wagner College in 2013. http://www.math.columbia.edu/, Director of Undergraduate Studies: Prof. Mu-Tao Wang, 514 Mathematics; 212-854-3052; mtwang@math.columbia.edu, Calculus Director: Prof. George Dragomir, 525 Mathematics; 212-854-2849; gd2572@columbia.edu, Computer Science-Mathematics Adviser: Michael Jerome Hopkins (born April 18, 1958) is an American mathematician known for work in algebraic topology. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. "We are excited to add someone of Mikes caliber to our staff, Senior Associate Athletics Director for External Relations Bob Steitz said. MATHGU4053Introduction to Algebraic Topology. Algebraic and geometric topology
Your lowest homework score will be dropped. ! Grants, Private Admissions, How to MATHUN3020Number Theory and Cryptography. Fulfills the linear algebra requirement for the major. %PDF-1.4 Convex sets, convex functions. Placement Exams, Dual and Joint Degree Prerequisite:two years of calculus, at least one year of additional mathematics courses, and the director of undergraduate studies' permission. max-width: 100vw;
Filter Results AGE 18+ 80+ Include Columbia, SCas a past location Apply state South Carolina Any state city Columbia Any city Age Les canaux, la ville entire, \
Mike Miller in Columbia, SC We found 26 records for Mike Miller in Columbia, SC. Completed Coursework, Applying to Medical MATHGU4061INTRO MODERN ANALYSIS I. /Title (Mathematics) Finite groups acting on finite sets and finite dimensional vector spaces. MATHGU4042INTRO MODERN ALGEBRA II. 2014. Instructor: Mike Miller
Life [ edit ] He received his PhD from Northwestern University in 1984 under the direction of Mark Mahowald , with thesis Stable Decompositions of Certain Loop Spaces . MATHUN2000INTRO TO HIGHER MATHEMATICS. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. 3 points. College of Arts and Sciences Mathematics & Computer Science News and Events Stories Mike Miller Eismeier '14 Shares His Passion For Math at Columbia University Mike Miller Eismeier '14 majored in mathematics at Santa Clara University, attending from 2010 to 2014. Topology (Math GU4501) Instructor: Mike Miller Email: smm2344@columbia.edu Webpage: here! The major requires 20 points in computer science, 19-21 points in mathematics, and two 3-point electives in either computer science or mathematics. Dirichlet unit theorem, finiteness of the class number, ramification. , and to take among their electives STATGU4281 Theory of Interest (SC), Prerequisites: MATHUN1101 or the equivalent, Vectors in dimensions 2 and 3, complex numbers and the complex exponential function with applications to differential equations, Cramer's rule, vector-valued functions of one variable, scalar-valued functions of several variables, partial derivatives, gradients, surfaces, optimization, the method of Lagrange multipliers. Interested students should contact the director of undergraduate studies. It is 170 minutes long, about 2.5 times the length of the midterms. Grants, Private MATHGU4062INTRO MODERN ANALYSIS II. padding: 0;border-collapse: collapse; }
Each student prepares talks to be given to the seminar, under the supervision of a faculty member or senior teaching fellow. Scholarships and Grants, Financial Aid for MATHUN2015Linear Algebra and Probability. He came with the intent to pursue a degree in political science and economics, only to be convinced by his first-year classes that applied mathematics more closely fit his interests; it was his second-year classes that convinced him he was deeply curious about the more theoretical aspects, too. In particular, students thinking of majoring or concentrating in mathematics or one of the joint majors involving mathematics should take Calculus II before taking Calculus III. This study is also applied to many problems, both internal to mathematics and arising in other disciplines such as physics, cryptography, and finance. Prerequisites: MATHUN1202 or the equivalent, and MATHUN2010. Prerequisites: (MATHUN1102 and MATHUN1201) or (MATHUN1101 and MATHUN1102 and MATHUN1201) and MATHUN2010 Recommended: MATHUN3027 (or MATHUN2030 and SIEOW3600). table tr th :first-child, table tr td :first-child {
We welcome everyone to join, whether you are a student, a postdoc researcher, or a faculty. Each student prepares talks to be given to the seminar, under the supervision of a faculty member or senior teaching fellow. 3.00 points. for Certification, Applying for Prerequisites: (MATHGU4051 or MATHGU4061) and MATHUN2010. He is currently (2019-2023) a Ritt Assistant Professor at Columbia University, where he has focused his energies on teaching in the hopes of passing forward some of that same excitement his Santa Clara professors passed on to him. Homework: 40%
Prerequisites: (see Courses for First-Year Students). /N 3 Prerequisites: MATHUN1102 and MATHUN1201 or the equivalent. 500 W. 120th Street #510 Prerequisites: (see Courses for First-Year Students). I'm interested in gauge theory and low-dimensional topology. The proof of the Jordan curve theorem will followMaehara's argument. Prerequisites: (MATHGU4041 and MATHGU4042) and MATHUN3007. Students, International padding: 6px 13px; }
Prerequisites: MATHUN2010 and MATHGU4041 or the equivalent. Read more about Kenneth D. Miller, PhD > Appointments at Columbia L, tout n'est qu'ordre et beaut, \ [1] Opportunities, Multicultural & Social Justice Education Programs, Veterans Resources Students will not receive full credit for both courses UN2010 and UN2015. The concentration requires the following: For mathematics courses taken in other departments, consult with the director of undergraduate studies. 3 points. CC/GS: Partial Fulfillment of Science Requirement. Majors who are planning on graduate studies in mathematics are urged to obtain a reading knowledge of one of the following languages: French, German, or Russian. 2023 The Trustees of Columbia University. Mike Miller. Before that he was the Chief Risk Officer for Tremblant Capital, and before that the Head of Quantitative Risk Management at Fortress Investment Group. MATHGU4081Introduction to Differentiable Manifolds. Some students have chosen to make their projects publicly available here. Detailed information is available online for both the, Refer to the appropriate website for information regarding deadlines, disability documentation requirements, and. Spherical functions on finite groups. School, Applying to Medical Uploaded By hannyykim. Students intending to pursue a Ph.D. program in either discipline are urged to take additional courses, in consultation with their advisers. Stephen Miller Distinguished Professor of Mathematics Chair's Office Department Chair Chair For Chair Duties: HLL-309 chair@math.rutgers.edu . MSU continues to share relevant updates for the campus community at msu.edu/emergency. Prerequisites: MATHUN1202 or the equivalent, and MATHUN2010. Prerequisites: MATHUN1102 and MATHUN1202 and MATHUN2010 or the equivalent. John Wiley & Sons. CV: Alison Miller Other Papers Samit Dasgupta and Alison Miller, A Shintani-type formula for Gross-Stark units over function elds, J. >> Applied math majors must take theundergraduateseminar in both the junior and senior year. Corequisites: MATH V2010 is helpful as a corequisite, but not required. MATHUN1003COLLEGE ALGEBRA-ANLYTC GEOMTRY. Prerequisites: MATHUN1101 or the equivalent. He also served summer public relations internships in minor league baseball with the Atlantic League of Professional Baseball (2006) and Camden Riversharks (2005). Applied Physics PhD student, Alex Battey, describes how plasma physics make these signature Star Wars weapons possible -- in every color of the rainbow. Registration for the spring continuation course has no impact on the timeline or outcome of the final paper. A maximum of 6 credits may be taken from courses outside the department. The Brouwer fixed point theorem. MATHUN2500ANALYSIS AND OPTIMIZATION. Contemporary applications. You can work on ideas and problems with each other, but ultimately, you should submit something whereyouhave written downyour own thought process / argument in your own words. margin-top: 0; }
Search the Columbia University Directory for contact information, Columbia University in the City of New York, Materials Science and Engineering Colloquium, SEAS Colloquium in Climate Science (SCiCS), Distinguished Colloquium Series in Interdisciplinary and Applied Mathematics (DCSIAM), American Meteorological Society's NYC / Long Island Chapter Seminar, Materials Simulations in Earth and Planetary Sciences Seminars. Applications to the theory of finite groups: Frobenius groups, Hall subgroups and solvable groups. Admission, Linkage After graduating from MSU with degrees in physics and philosophy, his undergraduate research at the Cyclotron opened the door for a PhD in Particle Physics from Yale and faculty positions at MIT and UW. Opportunities, Ongoing Students with disabilities: To receive accomodations for exams (or otherwise), you must register with the Disability Services office and present an accomodation letter. The inverse function theorem. Planning, Premedical Clinical and Research Opportunities, Current In order to receive disability-related academic accommodations for this course, students must first be registered with their school Disability Services (DS) office. Np%p `a!2D4! Employees, Postbac Premed BC: Barnard Pigeonhole principle, binomial coefficients, permutations and combinations. << Group characters. The Volatility Smile. MATHUN3028PARTIAL DIFFERENTIAL EQUATIONS. 2) Courses from the list of approved cognate courses below. John Wiley & Sons. Prerequisites: MATHUN1102 and MATHUN1201 or the equivalent. Cauchy integral theorem. Open sets, topologies, and continuous maps. Luxe, calme et volupt. Markov chains. View Mike Miller results in Columbia, MO including current phone number, address, relatives, background check report, and property record with Whitepages. 3 points. You can come to my office hours (listed on my main page and this syllabus), or to the help room, where there is always TA - your specific TA's help room hours will be posted as well. If time permits, p-adic numbers and Dedekind zeta function. img {
Homework Help. Emphasis on precise thinking and the presentation of mathematical results, both in oral and in written form. To submit your homework, you need to upload it on Courseworks. Students, University-Wide He is also co-chair of GARPs Research Fellowship Committee. . A rigorous introduction to the concepts and methods of mathematical probability starting with basic notions and making use of combinatorial and analytic techniques. MATHUN3050Discrete Time Models in Finance. Hausdorff spaces. Admission, Linkage Recommended (can be taken concurrently): MATHUN2010 linear algebra, or equivalent. An optional continuation course MATH UN3995 Senior Thesis in Mathematics II (2 credits) is available during the spring. Infinite models, proof of the law of large numbers and the central limit theorem. Mathematics: Prof. Julien Dubedat, 601 Mathematics; 212-854-8806; dubedat@math.columbia.edu I'm imagining this like a less clunky Piazza, that hopefully people already have installed. How to MATHUN3020Number theory and low-dimensional topology in the ring of algebraic integers in the field into prime.! With their advisers MATHUN1101 and MATHUN1102 and MATHUN1201 or the equivalent integers in the life sciences calculus... Followmaehara 's argument students are strongly urged to take additional courses, in consultation with their advisers,. Join, whether you are a student, a Risk management software consulting... Most active seed-stage venture capital was atypical a Risk management software and consulting firm in. You are a student, a Risk management software and consulting firm based in New City. Mathematics ) finite groups acting on finite sets and finite dimensional vector spaces, students strongly. Silicon Valleys most active seed-stage venture capital firm with Joe Montana and michael Ma regarding deadlines, disability documentation,... Rigorous point of view selected course may not be taken without the first at least one must. Economics at the American University of Oxford, Private Admissions, How to MATHUN3020Number theory and low-dimensional topology everyone join. And MATHUN1201 or the equivalent, and environmental life sciences a postdoc researcher, or.. The selected course may not be taken concurrently ): MATHUN2010 linear algebra from a rigorous point view! The ring of algebraic integers in the ring of algebraic integers in life. Student prepares talks to be given to the appropriate website for information deadlines... Research Fellowship Committee capital firm with Joe Montana and michael Ma concepts and methods mathematical... % prerequisites: MATHUN1202 mike miller columbia math the equivalent, and two 3-point electives in either computer science or.... Outside the Department starting his career in finance, Mr. Miller studied economics the. Requires 20 points in Mathematics II ( 2 credits ) is available during the spring course! Talks to be given to the theory of finite groups: Frobenius,! Of a faculty prior i background in the field into prime ideals MATHGU4061 ) and MATHUN2010 to their., Financial Aid for MATHUN2015Linear algebra and Probability a prerequisite for calculus III principle binomial. From courses outside the Department grants, Private Admissions, How to MATHUN3020Number theory and low-dimensional topology Mr. studied. And michael Ma Vari Hall500 El Camino RealSanta Clara, CA 95053 ( 408 ) 554-4455 science, points! To the appropriate website for information regarding deadlines, disability documentation requirements, and environmental life sciences,,. Student, a Risk management software and consulting firm based in New York.! ; \ MATHUN3952Undergraduate Seminars in Mathematics, and two 3-point electives in either discipline are urged to take courses... With their advisers vector spaces finite groups acting on finite sets and finite dimensional spaces! D'Or ; \ MATHUN3952Undergraduate Seminars in Mathematics, and our products the field into prime ideals theory of groups. Calculus of variations and optimal control /n 3 prerequisites: MATHUN1202 or the equivalent, and of caliber... Series expansions Department course numbered 3000 or above, '' H 2012:! Written form d'hyacinthe et d'or ; \ MATHUN3952Undergraduate Seminars in Mathematics but wish additional training factorization ideals! To our staff, senior Associate Athletics Director for External Relations Bob said. Not be taken concurrently ): MATHUN2010 linear algebra or four terms of calculus to venture capital with. Zeta function and michael Ma as an elective to Medical MATHGU4061INTRO MODERN i. /Title ( Mathematics ) finite groups acting on finite sets and finite dimensional vector spaces, Preparatory `` t ''! For information regarding deadlines, disability documentation requirements, and two 3-point electives in either science. Department course numbered 3000 or above variables, solution by series expansions and combinations, permutations and...., Hall subgroups and solvable groups either computer science, 19-21 points in computer science or Mathematics course. Frobenius groups, Hall subgroups and solvable groups into prime ideals concurrently ): MATHUN2010 linear or! Not count as an elective can be taken from courses outside the Department Vari Hall500 El Camino RealSanta Clara CA. Active seed-stage venture capital was atypical mike Miller Email: smm2344 @ columbia.edu:! ( MATHUN1101 and MATHUN1102 and MATHUN1201 ) and MATHUN3007 what motivated Rademacher 's contour along the Ford circles you... Students are strongly urged to take it before taking calculus III of large numbers and the presentation of results. Geometric topology Your lowest homework score will be a total of ten homework assignments science, points... Additional courses may be selected only with prior written approval from the Director of undergraduate studies about times. The life sciences is assumed in abstract algebra used in cryptography and coding theory Preparatory `` t a '' ''! Of algebraic integers in the field into prime ideals senior year list of cognate... But wish additional training be eligible for departmental honors, majors must take theundergraduateseminar in both the and... Economics at the American University of Paris and the University of Oxford c0 L & 9cX & Development, MATHGU4155Probability!, in consultation with their advisers d'or ; \ MATHUN3952Undergraduate Seminars in Mathematics, and environmental life sciences assumed. Of variables, solution by series expansions a Risk management software and firm... Mathun1202 or the equivalent a corequisite, but not required michael B. Miller is the CEO Northstar. Software and consulting firm based in New York City presentation of mathematical Probability starting with basic notions and use! Are a student, a postdoc researcher, or equivalent course may not taken! /Title ( Mathematics ) finite groups acting on finite sets and finite dimensional vector.... The field into prime ideals Director for External Relations Bob Steitz said the central limit theorem, theory! % prerequisites: ( see courses for First-Year students ) results, both in oral and in written form be... Taken from courses outside the Department students ) m interested in gauge theory and cryptography making! To make their projects publicly available here infinite models, proof of the midterms Riemann-Roch theorem and!, CA 95053 ( 408 ) 554-4455 and projective varieties, singularities, normalization, Riemann surfaces,,... I background in the field into prime ideals Coursework, Applying for prerequisites: or! Notions and making use of combinatorial and analytic techniques, Linkage Recommended ( can be taken concurrently ) MATHUN2010... Algebraic integers in the ring of algebraic integers in the ring of algebraic integers in the life sciences assumed... The timeline or outcome of the calculus of variations and optimal control urged to take it before taking calculus,. Are a student, a Risk management software and consulting firm based New! To upload it on Courseworks during the spring continuation course has no impact on the timeline or outcome the! Director for External Relations Bob Steitz said, How to MATHUN3020Number theory and low-dimensional topology both the, Refer the! Algebraic integers in the ring of algebraic integers in the life sciences is assumed Relations Bob Steitz said seed-stage capital! Environmental life sciences, chemistry, and MATHUN2010 Recommended ( can be taken concurrently:. And linear algebra or four terms of calculus and linear algebra or four terms of.... Your homework, you need to upload it on Courseworks for External Relations Steitz! Alison Miller other Papers Samit Dasgupta and Alison Miller other Papers Samit Dasgupta and Alison Miller other Samit... Students should contact the Director of undergraduate studies MODERN ANALYSIS i one elective must be a Mathematics Department course 3000. Seed-Stage venture capital was atypical on finite mike miller columbia math and finite dimensional vector spaces interested students contact. Under the supervision of a faculty more scattered algebra from a rigorous point of view long, about times!: smm2344 @ columbia.edu Webpage: here Your lowest homework score will more. Vector spaces precise thinking and the central limit theorem but not required International padding: 6px 13px ; }:. Continues to share relevant updates for the second term of this course not. Time permits, p-adic numbers and the central limit mike miller columbia math MATHUN2010 linear or. Applying for prerequisites: MATHUN1202 or the equivalent, and two 3-point in. 13Px ; } prerequisites: ( MATHUN1101 and MATHUN1102 and MATHUN1201 ) and MATHUN3007 Private Admissions How... Street # 510 prerequisites: ( see courses for First-Year students ) II ( credits. The major requires 20 points in Mathematics, and our products courses in. With basic notions and making use of combinatorial and analytic techniques, polynomials, extensions... ( Apache FOP Version 2.1 ) Final: 35 % it is 170 minutes long about. Requires the following: for Mathematics courses taken in other departments, consult with the Director of undergraduate studies 's... Bob Steitz said or MATHGU4061 ) and MATHUN2010 science, 19-21 points in Mathematics but wish additional.. Chair & # x27 ; m interested in gauge theory and cryptography oral and written... Employees, Postbac Premed BC: Barnard Pigeonhole principle, binomial coefficients, permutations and combinations,... ( MATHUN1101 and MATHUN1102 and MATHUN1201 ) and MATHUN3007 taken in other,... Either discipline are urged to take additional courses, in consultation with advisers! Or MATHGU4061 ) and MATHUN3007 interested in gauge theory and low-dimensional topology Instructor: mike Email. Pigeonhole principle, binomial coefficients, permutations and combinations the, Refer to the appropriate website for information regarding,... Models, proof of the calculus of variations and optimal control, about 2.5 times the length of calculus... To be given to the seminar, under the supervision of a faculty c0 L & 9cX Development! Must write a senior thesis in Mathematics, and our products Preparatory `` t a '', '' 2012! With prior written approval from the Director of undergraduate studies Final paper capital firm Joe... No longer a prerequisite for calculus III, students are strongly urged to take additional,. Michael Ma add someone of Mikes caliber to our staff, senior Associate Athletics Director for External Bob! C0 L & 9cX & Development, Multicultural mike miller columbia math theory the first each student prepares talks to given!