Credit is granted for only one course among Math 216, 286, and 316. No credit for those who have completed or are enrolled in Math 412.

problems. Although I participate in some such fora, I feel that they have a major tendency to be Background and Goals: This course is a continuation of Math 395 and has the same theoretical emphasis. Quotient and dual spaces, inner product spaces, spectral theory. results of them. be quite generous. 295-396 is very difficult. your own language. students outside the course, you should be seeking general advice, not There will be an in class exam near the end of February, most Overview: This course has a bit of a scattered collection of It treats techniques of solution (exact and approximate), existence and uniqueness theorems, some qualitative theory, and many applications. Overview: This course has a bit of a scattered collection of topics, but is ultimately heading towards the construction of abstract manifolds and the proof of Stokes theorem. It provides an excellent background for advanced courses in mathematics.

295-296 is doable, but if you put the homework off til Monday or Tuesday you will have to pull an all nighter Thursday even when working in a group. for participation in the Friday discussions and in recording the 396. Metric spaces, basic point-set topology.

This course is a continuation of Math 395 and has the same theoretical emphasis. too explicit in their help; you can read further thoughts of mine here. The format involves little formal lecturing, much laboratory work, and student presentations discussing partial results and approaches. Teaching Assistants: Wenyu Jin (wyjin AT umich) The discussion section will meet Wednesdays 4:00-5:00, in a No credit after Math 471 or Math 472. I don't intend for you to need to consult books and papers outside �G�F3�V����j��W���������ի7+f)�V���w¬^]�~.�^�7�b�+D���?vm}�X+��Ŀ����E��6u�o��wW����5�}��o��%��KI��D)�����-M:-C��9��O{����07�����_Y4�n����(]T��[וJ�*a��:�a:�!��'Ԑ�߷�ǫ������b C�!�ݝ>��hZ���*���P��~b�Wk� 3� �4];茽�~U���IV~���ݡ������Y��0%N"��u��\�%��r�f�����Y���67�R�"L�Ě~)_M��Dr�tAOt�t6�Qh�-�Z��L����.��)t�p_{��k�>xr2����0��' ���B��6-����>lP����vz+ґ5#Z�HJY^i�W#0���D�i@��.��t���6w����kCt�xנ9�dL� ����� �V��Q^MD����)Ch�ϧ! Notes I: Parametric curves Let Idenote an interval in R. It could be an open interval (a;b), or a closed interval [a;b], or semi-closed [a;b);(a;b]. The course is a hands-on introduction to various topics in probability. This term, I think I will more often use them for short Content: Submanifolds (with or without corners) of Euclidean space, abstract manifolds, tangent and cotangent spaces, immersion/submersion theorems. /Length 5216

This course is an introduction to Fourier analysis with emphasis on applications. Description: Honors Analysis II --- Differential and integral calculus of functions on Euclidean spaces. Brian 3 Credits. Proofs are given in class; homework problems include both computational and more conceptually oriented problems. I am also glad to make appointments to meet at other times. While the main effort will be to establish the foundations of the subject, applications will include the Fast Fourier Transform, the heat equation, the wave equation, sampling, and signal processing.

MATH 396. Math 351 may be used in stead of 451 for the Math of Finance and Risk Management major. /Filter /FlateDecode

assign students in pairs to write up the solutions to the problems for http://www.math.lsa.umich.edu/courses/389/, 2020 Regents of the University of Michigan. better/other understanding of the definitions and concepts, not Problems are chosen to be accessible to undergraduates. location to be determined. Math. Careful planning is essential. More advanced students, such as those who have completed Math 396, may substitute higher level courses with the approval of a major advisor. Inverse/implicit function theorems, immersion/submersion theorems.

First-order equations: solutions, existence and uniqueness, and numerical techniques; linear systems: eigenvector-eigenvalue solutions of constant coefficient systems, fundamental matrix solutions, nonhomogeneous systems; higher-order equations, reduction of order, variation of parameters, series solutions; qualitative behavior of systems, equilibrium points, stability. Conrad's notes are quite impressive. I will drop the lowest two homework grades. III. deRham cohomology, Riemannian metrics, Hodge star operator and the standard vector calculus versions of Stokes' theorem. This is a survey course of the basic numerical methods which are used to solve practical scientific problems. Topics will include properties of complex numbers, the Discrete Fourier Transform, Fourier series, the Dirichlet and Fejer kernals, convolutions, approximations by trigonometric polynomials, uniqueness of Fourier coefficients, Parseval's identity, properties of trigonometric polynomials, absolutely convergent Fourier series, convergence of Fourier series, applications of Fourier series, and the Fourier transform, including the Poisson summation formula and Plancherel's identity. �Nhl�)�w�z�l���c�_W�7����������&K�@�s*Ĉ�U����>����f��^�����|#?E�v���D��7Bk�h���$S�ʇ$B�3]'��7-J�Z(�!N�n�M��r���*��+e��n��/�U�+�2�U �����e�JÇ��h�k�W͵��0������@�e�&���2ɦ� ����u}�X}��7aD�2vm��(����`/V�R��T�k��:��_�;����nF9�'�e3o�-�q��pt�!�G{������e}*)�9K=�����2�D�2�,^3�nq�N�d�����(Y�6|�۳J��^����W��3�q%��� ��z�ݥ��c�K�%j�� Engin 101; and one of Math 216, 286, or 316; and one of Math 214, 217, 417, or 419. No credit granted to those who have takend or are enrolled in Math 485. These are all important both in theoretical probability, statistics and real world applications, and the course pursues these ideas from conceptual and applied points of view. You may post questions asking for clarifications solutions to the problems. Seeking problem solutions from people and sources outside this course,

and alternate perspectives on concepts and results we have covered. The numerical score will be computed as follows: This course is a continuation of the sequence Math 295-296 and has the same theoretical emphasis. likely Wednesday the 21st. Floating point arithmetic, Gaussian elimination, polynomial interpolation, spline approximations, numerical integration and differentiation, solutions to non-linear equations, ordinary differential equations, polynomial approximations. Logic and techniques of proof, sequences, continuous functions, uniform continuity, differentiation, integration, and the Fundamental Theorem of Calculus. on Fridays in class. Students are required to have taken Math 217, which should provide a first exposure to this style of mathematics. The course is conducted using a discussion format. provided (1) you list all people and sources who aided you, or %���� 3 Credits. The course content is similar to that of Math 451, but Math 351 assumes less background. 1518 CC Little. Here a;bare real numbers or in nity symbols 1 ;1. stream �9fGp�!7�"]O��9

Students are expected to understand and construct proofs. manifolds and the proof of Stokes theorem. If you seek help from mathematicians/math plagiarism and will meet severe consequences. This is an introduction to differential equations for students who have studied linear algebra (Math 217). Course website: Problems for projects are drawn from a wide variety of mathematical areas, pure and applied. Topics covered include problem solving, sets and functions, numeration systems, whole numbers (including some number theory), and integers. Special Courses The special Mathematics of Finance courses must include Math 423, 474, 471 or 472 (472 is preferred), and 526. There is tea time in the math commons room at 4:00 everyday (you will be familiar with it soon enough mwuahahahaha) where you can steal cookies from grad students. Related Courses. Universities » University of Michigan (UM) » MATH - Mathematics » 396 - Honors Analysis II » Prof. Ratings & Grades. Noah and Jin will hold office hours Thursday 5:30-6:30 in the Nesbitt Instead, each topic is studied with the ultimate goal being a real-world application. �0jGJs�۾�XOM�63������ @~��B��G�y^Y��w���J�E9��[��^��2�Lg��9��G���O&�wY�����芴��Č��tn�v�ׂ��K��\7���Ϙ The course also can be viewed as a way of deepening one’s understanding of the 100-and 200-level material by applying it in interesting ways. Partitions of unity, vector fields and differential forms on manifolds, exterior differentiation, integration of differential forms. Applications to physical problems are considered throughout.

With its few prerequisites and broad interest, it is also an ideal course for students wanting to explore mathematical thinking at a higher level. Webpage: http://www.math.lsa.umich.edu/~speyer/396. Each number system is examined in terms of its algorithms, its applications, and its mathematical structure. Student work expected: I will assign weekly problem sets, due

Office Hours: I will hold office hours 2844 East Hall, or directly copying solutions from your fellow students, is

k-forms. Topics in linear algebra: tensor products, exterior and symmetric powers, Jordan and rational canonical forms. provide help, as are your TA's Noah Luntzlara and Wenyu Jin.

topics that tie to the rest of the material, rather than take on a Grading: I will combine your grades into a numerical score, MATH 396 - Honors Analysis II at University of Michigan. Sets and functions, relations and graphs, rings, Boolean algebras, semi- groups, groups, and lattices. Integration in Euclidean space, Fubini's theorem, change of variables formula. This course, together with its sequel Math 489, provides a coherent overview of the mathematics underlying the elementary and middle school curriculum. You MAY NOT post homework problems to internet fora seeking Math 396 - Honors Analysis II. << room. 3 Credits. topics, but is ultimately heading towards the construction of abstract The course is designed to show you how new mathematics is actually created: how to take a problem, make models and experiment with them, and search for underlying structure. We'll then discuss the formalism of differential normal form. Submanifolds (with or without corners) of Euclidean space, abstract manifolds, tangent and cotangent spaces, immersion/submersion theorems. Math 295-296-395-396 is the most theoretical and demanding honors math sequence. and Noah Luntzlara (nluntzla AT umich).