Honors Mathematics II:

Professor Karen E. Smith

Course assistant: Ruthi Hortsch

Intended audience: super smart, hardworking freshman who survived Math 295 and want more!

Course Objective: To introduce students to the art and practice of mathematics while studying linear algebra, among many other topics.

Prerequisites: Math 295

The lectures for the course are MTWF at 1 pm in 4088. The discussion section is Monday 5-6 (led by Ruthi, this is not optional but a part of the course.)

The professor has office hours immediately after class on mondays and wednesdays; the course assistant has office hours thursdays 5-6. Both are happy to schedule alternate hours if you can't make these.

Text: Spivak, Calculus, Edition 4, and Hoffman and Kunze, Linear Algebra.

Some topics we will cover: Sequences and series of functions, power series, uniform convergence of functions, real analytic functions. The complex numbers. Vector spaces, bases, linear transformations, dual spaces, determinants, traces, eigenvalues, inner-product spaces. Rudiments of Multilinear Calculus: Limits and continuity in Euclidean space, derivative as a linear map, Chain rule.

Details about course organization on the Math 296 Course Information Sheet

The Daily Update, a summary of what was discussed in class each day, including assignments and quiz announcements.

NEW! Professsor Smith's notes on Representation Theory , for a course she gave for math and (mostly) physics students in Finland. (Note: this is possibly a book in progress, so please report all typos and unclear explanations if you want your name mentioned in it!)

A write up about the idea of QUOTIENT OBJECTS , written by Ruthi after seeing how many people incorrectly proved that $\mathbb F_p$ is a field on Homework 6. PLEASE LOOK AT IT!

Make-up Quiz 5 , mandatory for all scoring below 7 on Quiz 5, to be turned in by Monday March 14. Note: the numbers are changed; it is not literally the same.

Groups and their Representations Worksheet . Cosets and Quotient Groups Worksheet .

EXAM 2 will be in class on Friday March 25. The problems will be distributed the previous friday.

The FINAL EXAM will be THURSDAY APRIL 21, 4-6, in the usual classroom. The problems will be distributed the previous friday.

Notes by Nick Wasylyshyn from Professor Andrey's lectures on Complex Analysis: Edited Version including all four lectures , and then also unedited versions of each day: Monday , Tuesday , Wednesday , Friday ,

Problem Sets: Set 1 , Set 2 , Set 3 , Problems for Exam 1 , Set 4 , Set 5 , Set 6 , Set 7 , Set 8 , Exam 2 Problems , Set 9 , Set 10 , Set 11 , Final Exam Problems ,