Math 15900, Section 43, Autumn 2015

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,

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 11:30-12:20, Eckhart 202.

Problem sessions: Mondays 18:00-19:00, Eckhart 207.

Office hours: Tuesday 17:00-18:00, Wednesday 17:00-18:00, or by appointment (preferred).

Important dates:

General policy: There will be two in-class hour tests 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 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:

  1. 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.
  2. 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 1pm in the pigeonhole in Eckhart basement (or in class).

Reader: Noah Kahrs,


Homework 1 due October 7th (corrected 10/5).
Homework 2 due October 14th (note correction!!).
Homework 3 due October 21st (typos fixed 10/15, 10/16).
Homework 4 due October 28th (typo fixed 10/23).
Homework 5 due November 4th.
Homework 6 due November 11th.
Homework 7 due November 18th (typo q6 fixed 11/16. Error q10 fixed 11/17.).
Homework 8 due November 25th.
Homework 9 no due date; not graded.


Midterm 1 was sat on Wednesday 21st October. The median score was 27/30 and the mean was 23.6/30.
Midterm 2 was sat on Wednesday 18th November. The median score was 33.5/40 and the mean was 32/40.
The final was sat on Friday 11th December.


Notes, with thanks to Adel Rahman for allowing me to post them here.
Axioms for number systems.
Some of the "further reading" on Gowers's website might be enlightening.
This book appears to be a nice introduction to mathematical proofs.