## Welcome to Tom Roby's Math 215 homepage! (Fall 2006)

(last updated: 23 October 2006)

### Class Information

COORDINATES: Lectures meet Tues/Thur. 12:30--1:45 in MSB 215 (really!). The registrar calls this Sec 001, #4792

PREREQUISITES: Math 213 (Intro to Proofs) and Math 227 (Applied Linear Algebra)

TEXT: Sheldon Axler, Linear Algebra Done Right, 2nd Ed. Springer

WEB RESOURCES: The homepage for this course is http://www.math.uconn.edu/~troby/Math215F06/. It will include a copy of the syllabus and list of homework assignments. I will keep this updated throughout the quarter.

This course will have a WebCT/Vista homepage (once I get it setup), with discussion forums that you may to use. Go to WebCT at http://webct.uconn.edu/. For help with WebCT go to http://lrc.uconn.edu/LRC_aboutWebCT.htm, or visit the Learning Resource Center on Level 1 of the Homer Babbidge Library.

The breakdown of points is:

Midterm Final Homework Quizzes
25% 30% 20% 25%

EXAMS: The exam dates are already scheduled, so please mark your calendars now. No makeups will be given; instead if you have an approved reason for missing an exam, the final will count for the appropriately higher percentage.

CONTENT: Linear algebra is a beautiful and important subject that lies at the heart of mathematics. It can be approached in a very concrete way, through matrix calculations as in Math 227, but to gain a deep understanding requires a more abstract viewpoint. It's an everyday occurence for a mathematician to want to compute an example of something and find that in the end it boils down to a linear algebraic computation best done via Matlab, Maple, or Mathematica. Linear algebra has applications all across mathematics, science, engineering, statistics and the social studies, which is why we teach so many sections of Math 227. Within mathematics, we will see how it can help us do such things as fit a degree n polynomial through any n+1 points in R^2 or find a formula for the nth Fibonacci number.

LEARNING GOALS: This is a second course in linear algebra, where we focus on the abstract concepts and minimize computations. I will assume that you remember (or can quickly review) how to do matrix computations as we need them. This course will help prepare you for even more theoretical courses to come and help you see the power of mathematics done this way. We will work consistently on writing careful proofs, extending the work you've done in Math 213 and elsewhere.

LEARNING: The only way to learn mathematics is by doing it! Complete each assignment to the best of your ability, and get help when you are confused. Come to class prepared with questions. Don't hesitate to seek help from other students. Sometimes the point of view of someone who has just figured something out can be the most helpful.

DISABILITIES If you have a documented disability and wish to discuss academic accommodations, or if you would need assistance in the event of an emergency, please contact me as soon as possible.

HOMEWORK: Homework will be assigned weekly on the schedule below. You can ask questions about the homework in one of the WebCT/Vista forums. Except for routine computations, you should always give reasons to support your work and explain what you're doing. I will collect homework and grade a pseudorandom sample of it.

You may find some homework problems to be challenging, leading you to spend lots of time working on them and sometimes get frustrated. This is natural. I encourage you to work with other people in person and via Vista. It's OK to get significant help from any resource, but in the end, please write your own solution in your own words. Copying someone else's work without credit is plagiarism and will be dealt with according to university policy. It also is a poor learning strategy.

215 LECTURE AND ASSIGNMENT SCHEDULE
Date Sections Topics
8/29 T Ch. 1 Vector Space Def. & Basic Properties HW1 (due 9/6): #4,7,8,12,13,14
8/31 R Ch. 1 Subspaces & Sums Quiz #1 on Ch. 1
9/5 T Ch. 2 Span & Lin. Indep.
9/7 R Ch. 2 HW2 (due 9/14): p. 35ff: #2, 4, 5, 8, 9
9/12 T Ch. 2 Bases & Dimension
9/14 R Ch. 2-3 Linear Maps: Null Space & Range HW3 (due 9/21): p. 35ff: 11,13,14; p. 59: 1,2,5
9/19 T Ch. 3 Linear Maps HW4 (due 9/28) p. 59ff: 7,11,14,17,22,25
9/21 R Ch. 3 Linear Maps
9/26 T Ch. 3 Matrices & Invertibility
9/28 R Ch. 5 Eigenvalues & Eigenvectors HW5 (due Mon 10/9 17:00): Ch4: #2,4,5 (p.73); Ch5: #2,3,5 (p.94)
10/3 T Ch.4 Polynomials over R and C
10/5 R Ch. 5 Eigenvalues & Triangular Matrices HW6 (due Fri 10/13) Ch. 5 (p.94-6): 8, 9, 17, 19, 23
10/10 T Ch. 5-6 Eigenspaces and Inner-Product Spaces
10/12 R Ch. 1-5 Review for Midterm Do practice midterm by today
TUESDAY 17 OCTOBER: MIDTERM EXAM
10/19 R Ch. 6 Inner Product Spaces HW7: Ch. 6: #2,3,4,10,11
10/24 T Ch. 6 Orthonormal Bases; Gram-Schmidt
10/26 R Ch. 6 Ortho. Projections and Minimization HW8: Ch 6 #13,14,15,17,19
10/31 T Ch. 6 Linear functionals & Adjoints
11/2 R Ch. 7 Self-Adjoint & Normal Ops; Spectral Thm.
11/7 T Ch.7 Real Spectral Thm HW9: Ch 7 #6,8,9,10,12,13
11/9 R Ch. 7 Normal ops in Real VS
11/14 T Ch. 8 Generalized Eigenvectors
11/16 R Ch. 8 Characteristic & Minimal Polys HW10: Ch. 8 #2,3,5,9,15,22
11/28 T Ch. 10 Trace & Determinant HW11: Ch. 10 #6,7,9,16,25,"det in plane"
11/30 R Ch. 10 Determinant & Volume
12/5 T Conrad Handout The Hurwitz 1,2,4,8 Thm
12/7 R Review Day
FRIDAY 15 DECEMBER 10:30-12:30 FINAL EXAM IN MSB 215