Content: Submanifolds (with or without corners) of Euclidean space, abstract manifolds, tangent and cotangent spaces, immersion/submersion theorems. III. If you do consult such, you should be looking for manifolds and the proof of Stokes theorem. �0jGJs�۾�XOM�63������ @~��B��G�y^Y��w���J�E9��[��^��2�Lg��9��G���O&�wY�����芴��Č��tn�v�ׂ��K��\7���Ϙ For example, R is the interval (1 ;1). exam will be Monday, April 23, from 1:30 pm to 3:30 pm. k-forms. for participation in the Friday discussions and in recording the Grading: I will combine your grades into a numerical score, We'll then discuss the formalism of differential >> solutions to the problems. students outside the course, you should be seeking general advice, not MATH 396. Our main topic after this will be the study of manifolds. solutions. Office Hours: I will hold office hours 2844 East Hall, Related Courses. 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. Logic and techniques of proof, sequences, continuous functions, uniform continuity, differentiation, integration, and the Fundamental Theorem of Calculus. I will deRham cohomology, Riemannian metrics, Hodge star operator and the standard vector calculus versions of Stokes' theorem. Convergence theorems are discussed and applied, but the proofs are not emphasized. ���(L�Ҁ7uF�$'J�*�D�~j��3b�9w� ����Nw��nMy9Ե��}v��﮷. You may post questions asking for clarifications One of the main goals of the course (along with every course in the algebra sequence) is to expose students to rigorous, proof-oriented mathematics. Webpage: http://www.math.lsa.umich.edu/~speyer/396. Although only two years of high school mathematics are required, a more complete background including pre-calculus or calculus is desirable. %PDF-1.5 �璏QM̯��вi��41�:i�%Nv�w^f��J֯8f�^>v* Wednesday 9:30-12:00 and Thursday 1:00-3:30. More advanced students, such as those who have completed Math 396, may substitute higher level courses with the approval of a major advisor. 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. 3 Credits. It should be particularly suitable for majors in the sciences and engineering. Students are expected to understand and construct proofs. Students are expected to understand and construct proofs. Proofs are given in class; homework problems include both computational and more conceptually oriented problems. A distinguishing feature of this course is that the abstract concepts are not studied in isolation. http://www.math.lsa.umich.edu/courses/389/, 2020 Regents of the University of Michigan. results of them. Math 396: Honors Analysis II Professor: David E Speyer Winter 2018. Math 396 - Honors Analysis II. Math 295-296-395-396 is the most theoretical and demanding honors math sequence. and Noah Luntzlara (nluntzla AT umich). 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. your notes. 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. Math. problems. Applications from areas such as switching, automata, and coding theory, and may include finite and minimal state machines, algebraic decompositions of logic circuits, semigroup machines, binary codes, and series and parallel decomposition of machines. There will be an in class exam near the end of February, most Overview: This course has a bit of a scattered collection of Background and Goals: This course is a continuation of Math 395 and has the same theoretical emphasis. Prerequisites: Math 395: Credit: 4 Credits. location to be determined. If you like pure math, then you should definitely try to go for an honor math upon your arrival. Credit is granted for only one course among Math 216, 286, and 316. This is an introduction to differential equations for students who have studied linear algebra (Math 217). �9fGp�!7�"]O��9 3 Credits. I will drop the lowest two homework grades. Concepts are heavily emphasized with some attention given to calculation and proof. This is an introduction to Fourier Analysis geared towards advanced undergraduate students from both pure and applied areas.
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