# Math 15900, Section 55, Winter 2016

This is a one-quarter long introduction to
mathematical proof, analysis, and linear algebra. 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.

**Text:** Paul Sally, Tools of the Trade, ISBN 978-0-8218-4634-6. In particular, sections 1.1-1.7, 3.1, 3.2, 3.4, 3.6 and 2.1-2.4.

**Lectures:** MWF 12:30-13:20, Rosenwald 015.

**Problem sessions:** Wednesdays 17:00-18:00, Eckhart 308.

**Office hours:** Mondays 15:00-16:00, Fridays 15:00-17:00, or by appointment.

**Important dates:**

- Final exam: Tuesday 15th March, 16:00-18:00.
- Midterm 1: Monday 25nd January
- Midterm 2: Monday 15th February

**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 January 13th.

Homework 2 due January 20th.

Homework 3 due January 27th.

Homework 4 due February 3rd. Corrected 2/1.

Homework 5 due February 10th.

Homework 6 due February 18th.
Homework 7 due February 24th.

Homework 8 due March 2nd.

Homework 9 not graded.

Here is a practice final.
## Exams

Midterm 1 was sat on Monday 25th January. The median score was 17.5/30 and the mean was 16.1/30.

Midterm 2 was sat on Monday 15th February.

The final was sat on Tuesday 15th March.
## Resources

Here is a list of the axioms for rings, fields etc.

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

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