# Math 15900, Section 57, Spring 2016

This is a one-quarter long introduction to
mathematical proof, analysis, and multivariable calculus. It is aimed at preparing students for more advanced analysis and algebra
courses such as Math 20300.
**Instructor:** Jack Shotton, Eckhart 333, jshotton@math.uchicago.edu

**Texts:** Paul Sally, Tools of the Trade. In particular,
sections 1.1-1.7, 3.1, 3.2, 3.4, 3.6 and 2.1-2.4.

Spivak, Calculus on Manifolds

**Lectures:** MWF 12:30-1:20pm, Social Sciences 108

**Problem sessions:** M 6-7, Eckhart 308. W 6-7 Eckhart 202.

**Office hours:** 5pm-6pm M, T, W, Th

**Important dates:**

- Final exam: Thursday 9th June, 16:00-18:00
- Midterm 1: Monday 18th April
- Midterm 2: Monday 16th May

All exams take place in Social Sciences 108 (the same place as class).
**General policy:** There will be two in-class hour tests (midterms) and a final
exam, as well as weekly homework. You should feel free (encouraged!) to work on homework together,
but writeups must be independent. The material for the hour-tests will be theorems, definitions and
proofs that I did in class, together with questions similar to those on the homework sheets. For
the determination of the final grade, the weighting will be: 50% on the final, 20% on each hour
test, and 10% on the homework.

It is the policy of the Department of Mathematics that the following rules apply to final
exams in all undergraduate mathematics courses:

- The final exam must occur at the time and place designated on the College Final Exam
Schedule. In particular, no final examinations may be given during the tenth
week of the quarter, except in the case of graduating seniors.
- Instructors are not permitted to excuse students from the scheduled time of the final exam
except in the case of an incomplete.

**Homework:** This will be posted on here weekly, and due each Wednesday at 2pm in the
pigeonhole in Eckhart basement (or in class).

**Reader:** Noah Kahrs, nkahrs@uchicago.edu.

## Homework

Homework 1 due April 6th.

Homework 2 due April 13th.

Homework 3 due April 20th.

Homework 4 due April 27th.

Homework 5 due May 4th.

Homework 6 due May 11th.

Homework 7 due May 24th.

Homework 8 not due.
## Exams

Midterm 1 was sat on April 18th. The median score was 19/30.

Midterm 2 was sat on May 16th. The median score was 21/30.

The final was sat on June 9th. The median score was 38/60.
## Resources

Here is a list of the axioms for fields.

Equivalence classes

Algebra of limits

Some of the "further reading"
on Gowers's website might be
enlightening.

This book appears to be a nice introduction to mathematical proofs.