Josh Southerland

Course Summary

This is a first course in mathematical reasoning, largely focused on reading and writing rigorous mathematical proofs. As such, this is an introduction to the techniques commonly assumed in upper-level, proof-based math courses. Topics include logic, proof techniques, set theory, functions, and cardinality.

Information

Syllabus

Academic Honesty Pledge

Instructor: Josh Southerland

Office Hours: via Zoom

Wednesday: 4:30-6:30 pm PDT (tentatively)

Office: Padelford (PDL), C-552

Contact: j s o u t h e r AT u w . e d u

Additional help is available outside of class and office hours at CLUE. Visit their website to find out more about online assistance.

Textbook and Lecture Notes

There is no required textbook for this course. I will provide a set of lecture notes for each week, and post them in the course schedule below. However, we will be roughly covering the same content in the following free textbooks.

An Introduction to Mathematical Reasoning by Matthew Conroy and Jennifer Taggart
Mathematical Reasoning: Writing and Proof, Version 2.1 by Ted Sundstrom

Technology Requirements

All lectures in this course will be recorded live on Zoom during the regularly scheduled class time. Additionally, all office hours, review sessions, quizzes and exams will be on Zoom. For additional Zoom and technology policies, refer to the syllabus.

A laptop or phone that will allow you to participate in Zoom video conference calls
Regular internet access
Browser that can access Gradescope, Canvas, and this course website
Gradescope Account
The ability to upload PDFs of written work (for example: phone apps that convert images to pdfs)

Homework

For homework, you will need to use Gradescope. All homework will require either written or typed solutions to a weekly problem set. All solutions must be uploaded to Gradescope prior to the deadline. There are no extensions, however, 20% of the total homework points will be dropped.

Canvas Quizzes

The weekly Canvas quizzes can be found on Canvas. These are short quizzes intended to check to make sure you are keeping up with the course content. Each quiz covers the prior week's lecture content.

Written Quizzes

Quiz 1: Wednesday, July 14

Covers course content from Weeks 1 and 2, which correspond to homeworks #1 and #2.

Quiz 2: Wednesday, August 4

Covers material from weeks 3, 4, and 5, which correspond to homeworks #3, #4, and #5.

Quiz 3: Friday, August 20

Covers material from weeks 6, 7, and 8, which correspond to homeworks #6, #7, and #8.

Course Schedule with Lecture Notes and Recordings (Under construction!)

Week	Monday	Tuesday	Wednesday	Thursday	Friday
Jun 21	Lecture Day Lecture 1: Logistics and Logic Lecture Notes: Week #1		Lecture Day Lecture 2: More on Logical Reasoning		Lecture Day Lecture 3: More on Logical Reasoning and a Kahoot Week 1 Review Questions
Jun 28	Lecture Day Lecture 4: Direct Proofs Lecture Notes: Week #2 Axioms for Homework! Canvas Quiz Quiz Open 4:00 am PDT - 5:00 pm PDT 10 minutes Answers released at 5:15 pm PDT Covers Week #1 Lecture Notes	Submit Academic Honesty Pledge By 11:59pm on Gradescope	Lecture Day Lecture 5: Contrapositive Proofs Office Hours 4:30-6:30 pm PDT Link on Canvas Homework #1 Due See Week #1 Lecture Notes Submit on Gradescope		Lecture Day Lecture 6: Contradiction Proofs
Jul 5	Holiday		Lecture Day Lecture 7: Quantifiers Lecture Notes: Week #3 Canvas Quiz Quiz Open 4:00 am PDT - 5:00 pm PDT 8 minutes Answers released at 5:15 pm PDT Covers Week #2 Lecture Notes Office Hours 4:30-6:30 pm PDT Link on Canvas Homework #2 Due See Week #2 Lecture Notes Submit on Gradescope Answer Key		Lecture Day Lecture 8: Quantifiers
Jul 12	Lecture Day Lecture 9: Sets Lecture Notes: Week #4 Canvas Quiz Quiz Open 4:00 am PDT - 5:00 pm PDT Answers released at 5:15 pm PDT Covers Week #3 Lecture Notes	Extra Office Hours Time TBA	Quiz 1 12:00-12:20pm PDT Upload to Gradescope by 12:30 pm PDT Covers Week #1, Week #2 Answer Key Lecture Day Lecture 10: Sets Office Hours 4:30-6:30 pm PDT Link on Canvas	Homework #3 Due See Week #3 Lecture Notes Submit on Gradescope Answer Key	Lecture Day Lecture 11: Sets
Jul 19	Lecture Day Lecture 12: Maps Lecture Notes: Week #5 Canvas Quiz Quiz Open 4:00 am PDT - 5:00 pm PDT Answers released at 5:15 pm PDT Covers Week #4 Lecture Notes		Lecture Day Lecture 13: Maps Office Hours 4:30-6:30 pm PDT Link on Canvas Homework #4 Due See Week #4 Lecture Notes Submit on Gradescope Answer Key		Lecture Day Lecture 14; Injective, Surjective, and Bijective
Jul 26	Lecture Day Lecture 15: Proof Problems Lecture Notes: Week #6 Canvas Quiz Quiz Open 4:00 am PDT - 5:00 pm PDT Answers released at 5:15 pm PDT Covers Week #5 Lecture Notes		Lecture Day Lecture 16: Proof Problems Office Hours 4:30-6:30 pm PDT Link on Canvas Homework #5 Due See Week #5 Lecture Notes Submit on Gradescope Answer Key		Lecture Day Lecture 17: Proof Problems
Aug 2	Lecture Day Lecture 18: Example + Cardinal Equivalence Lecture Notes: Week #7 Canvas Quiz Quiz Open 4:00 am PDT - 5:00 pm PDT Answers released at 5:15 pm PDT Covers Week #6 Lecture Notes	Extra Office Hours Time TBA	Quiz 2 12:00-12:20pm PDT Upload to Gradescope by 12:30 pm PDT Covers Weeks #3, #4, #5 Answer Key Lecture Day Lecture 19: Cardinal Equivalence Office Hours 4:30-6:30 pm PDT Link on Canvas	Homework #6 Due See Week #6 Lecture Notes Submit on Gradescope	Lecture Day Lecture 20: Countable sets
Aug 9	Lecture Day Lecture 21: Uncountability of the Reals Lecture Notes: Week #8 Canvas Quiz Quiz Open 4:00 am PDT - 5:00 pm PDT Answers released at 5:15 pm PDT Covers Week #7 Lecture Notes		Lecture Day Lecture 22: Partitions Office Hours 4:30-6:30 pm PDT Link on Canvas Homework #7 Due See Week #7 Lecture Notes Submit on Gradescope Answer Key		Lecture Day Lecture 23: Equivalence Classes
Aug 16	Lecture Day Lecture 24: Schroeder-Bernstein Theorem Canvas Quiz Quiz Open 4:00 am PDT - 5:00 pm PDT Answers released at 5:15 pm PDT Covers Week #8 Lecture Notes		Lecture Day Lecture 25: The Halting Problem Office Hours 4:30-6:30 pm PDT Link on Canvas Homework #8 Due See Week #8 Lecture Notes Submit on Gradescope Answer Key	Extra Office Hours Time TBA	Quiz 3 12:00-12:40pm PDT Upload to Gradescope by 12:50 pm PDT Covers Weeks #6, #7, #8 Answer Key

Week

Monday

Tuesday

Wednesday

Thursday

Friday

Jun 21

Lecture Day