# Math 432/532

## Winter 2020

The problems in parentheses are optional for undergraduates, required for graduate students.
• Syllabus.
• Homework 1 (due 1/10): §1.1 #7, 10, 11, (18). Solutions: pdf, tex.
• Reading 1 (due 1/12): §§1.1–1.3.
• Homework 2 (due 1/17): §1.2 #5, 7, 8, (12). Solutions: pdf, tex.
• Reading 2 (due 1/19): §§1.4, 1.5.
• Homework 3 (due 1/24): §1.3 #5, 8, (10). Solutions: pdf, tex.
• No reading for 1/26.
• Homework 4 (due 1/31): §1.4 #1, 12. §1.5 #2, (6). Solutions: pdf, tex.
• Reading 3 (due 2/2): §§1.6, 1.7 through the first paragraph of page 41. (Leave “Let us illustarte…” for next week.)
• Homework 5 (due 2/7): §1.5 #8. §1.6 #1, 2. Solutions: pdf, tex.
• Midterm 1, solutions, tex.
• No reading for 2/9.
• Homework 6 (due 2/14): §1.6 #7, 9. §1.7 #4, 5. Solutions: pdf, tex.
• Problems on the space of matrices (532 only, due 2/28): pdf, tex.
• Reading 4 (due 2/16): Finish §1.7.
• Homework 7 (due 2/21): §1.7 #3, 13, 14, 15. Solutions: pdf, tex.
• Midterm 2, solutions, tex.
• Reading 5 (due 3/1): §1.8.
• Homework 8 (due 3/13): §1.8 #2, 6, 7, 8, 9, (14).
Additional problem for 532 students: Let mn, and let f: XRmn be a smooth function, where we view the target as m×n matrices. Suppose that for all x ∈ X, the matrix f(x) is surjective. Show that there is a smooth map g: XRnm, where we view the target as n×m matrices, such that f(x) g(x) = 1, where on the left-hand side we mean matrix multiplication and on the right we mean the m×m identity matrix. (Detailed hint given via email, using a partition of unity.)
• Take-home final exam: pdf, tex. Optional, due to coronavirus disruptions.