Math 308, Fall 2018
Bridge to Advanced Mathematics



Professor: Zajj Daugherty
Class: TuTh 9:30am–10:45am in NAC 6/113
Office hours: Thursday 11am-12pm in NAC 6/301. By arrangement only: Tuesday 4pm.
Textbooks: How to Think Like a Mathematician: A Companion to Undergraduate Mathematics, by Kevin Houston; Introduction to Mathematical Structures and Proofs, by Larry J. Gerstein; and Elementary Analysis: The Theory of Calculus, by Kenneth A. Ross.
Grades: Your grades will be based on homework assignments (15%), a portfolio (20%), and exams (65%). Exams: October 16 & 18, and December 6 & 11.

Homework 0: Due Tuesday 9/4. Email from your preferred email account with subject line "Math 308: Homework 0", including the following information:
(a) What name you like to go by, and how is it pronounced.
(b) What you're majoring in, and why.
(c) What your general long-term goals are.
(d) Something that you're really good at.
(e) A photo or a physical description of yourself to help me learn your name faster. ("That guy who doesn't say anything" isn't sufficient.)


Week 1
Read Preface and Chapters 1 & 2 of "How to think..."
Notes: [Tuesday (slides) (printout)] [Thursday (slides) (printout)]
Articles from class (access from on campus): A short elementary proof, Ramanujan, Rational Ratios, Lebesgue's Road, A Continuous Function.
Due 9/4: Homework 1 (pdf) (tex) (zip).
Solutions: (pdf) (tex) (zip).
Due 9/13: Homework 2 (pdf) (tex) (zip)
Week 2
Read Chapters 3 and 4 of "How to think...", and Guidelines for Good Mathematical Writing for Tuesday; Chapter 5 for Thursday.
Notes: [Tuesday (slides) (printout)] [Thursday (slides) (printout)]
Proofs without words:
Problem 1 (image), Problem 2 (image), Problem 3 (image).
Due 9/20: Homework 3 (pdf) (tex) (zip)
Hints: (a) hint 1, hint 2; (b); (c) hint 1, hint 2; (d) hint 1, hint 2, hint 3; (e); (f).
Week 3
No class on Tuesday
Read Chapters 6 and 7 of "How to think...".
Notes: [Thursday (slides) (printout)]
Due 9/27: Homework 4 (pdf) (tex) (zip)
Week 4
No class on Tuesday
Read Chapters 8 and 9 of "How to think...".
Notes: [Thursday (slides) (printout)]
Due 10/2: Homework 5 (pdf) (tex) (zip)

LaTeX guide

You will be expected to learn to type up your homework using LaTeX. You can either downlad and install LaTeX on your computer, or use a free online compiler like overleaf or share LaTeX (lots of other suggestions).

To get you started, download Homework 1 and try to get it to complile. There are also lots of great resources out there to help you learn. To see my code, the LaTeX files for notes and handouts on any of my other course pages can be found by replacing .pdf with .tex for most of my files. You can find another sample on my teaching page, and lots of sample code at The Not So Short guide to LaTeX is linked from my resources page. You can also look up symbols by drawing at detexify.

More guides to LaTeX, what it is, and how to get started:
- LaTeX beginners tutorial
- Introduction to LaTeX (Short Course given at the UIUC REU Number Theory Program, Summer 2001 - revised August 2004)
- Getting Started with LaTeX, by David R. Wilkins
- Overleaf's "getting started" help section
- YouTube videos from John Mayberry or Michelle Krummel