General Course Notes
In-class Handouts
- Contact Info Sheet (for getting contact info of a new group)
- Your First Mission (investigating polyhedra) and the polyhedron pictures
- A first proof (if n is even, then n squared is even), and a video of me talking through it
- A 2 minute video that addresses the issue of nested sets.
- Set game instructions and cards
- Worksheet on Cartesian products
- Worksheet on Subsets vs. Elements
- Video of an informal explanation of why the square root of 2 is irrational (Numberphile)
- Worksheet on Setting up Contradiction
- Info on studies about cognition and math:
- Worksheets on negation: Negation I (shoes and hats) and Negation II (numbers) and solutions to the latter.
- My video on if-then statements.
- My video on the Dystopian Perspective on negation of statements, particularly if-then statements.
- SPQR Logic Game: cards and instructions.
- Basic Truth Tables for filling in, and a filled version.
- Solutions for Quiz #4 (contradiction or pigeonhole).
- Logical Equivalence Worksheet
- Four-Colour/Graph Intro Warmup
- Graph Definition and Handshake Lemma
- PDF Presentation of Trees having n-1 edges and accompanying video
- Proof by Contrapositive Setup Sheet and solutions.
- Proof by Induction Setup Sheet.
- Functions Worksheet (Introduction to Functions)
- Proof that a function has an inverse if and only if it is bijective (with slots, and filled).
- Worksheet on relations.
Groupwork Assignments
- Blank Groupwork Report and LaTeX Source
- Groupwork Due January 26th
- Groupwork Due February 2nd (and accompanying video)
- Groupwork Due February 9th
- Groupwork Due February 16th
- Groupwork Due February 23rd
- Groupwork Due March 2nd
- Groupwork Due March 9th
- No groupwork Due March 16th
- Individualwork Due March 23rd
- Individualwork Due April 6th
- Groupwork Due April 13th
- Individualwork Due April 20th
Access your Grades
Please check your grades weekly on canvas. I will try to keep them up to date every week so you know which badges you have earned. Please check them for correctness and alert me to any errors. It is quite a complicated administrative task.
Textbook
- Official Text: Book of Proof, Richard Hammack.
- Textbook Website (free PDF)
Computing Resources
- Campus Computer Labs – Use Sage (via link below), Latex, Maple, Mathematica, Matlab etc.
- Search by software – e.g. tex, mathematica
- Latex – the only reasonable way to type math.
- Introduction to Latex – installing and how to type.
- Detexify – To find a symbol you want to know.
- Overleaf.Com – No need to install software or visit the lab – typeset online!
- Templates: tex file and expected output.
- Tex Stackexchange – question and answer service from the hive mind
- Wolfram Alpha – Simple math computation without learning a syntax.
- Sage – Free, sophisticated math software for indepth exploration.
- CU Sage Server – available with identikey.
- Ask Sage – question and answer service from the hive mind
- Sage’s Quick Reference Sheets to keep by your side.
General Math Resources
Note: the internet can in fact do your homework for you in many cases. So can your friends, your mother, and your tutor. That’s not the point. Study (and drink) responsibly.
- Study Math by Speaking It
- Tips on Doing Homework
- Tips on Reading your Textbook
- Dr. Math – Question answer service (by ‘Math Doctors’). Use the search box first; there’s a 99% chance someone has asked your question before.
- Mathematics at StackExchange – Question answer service (by the ‘hive mind’). Use the search box first; there’s a 98% chance someone has asked your question before.
- Math Forum Digital Library – Catalogue of web resources.
CU Resources
- The Undergraduate Mathematics Resource Center is in Math 175 (first floor of math building). Although tutors do not serve this course, an area has been set up where you can meet your peers to work together.
- A tutor list is available.