Notes – Introduction to Mathematical Thinking DeCal

Go to the course website here

Here, we link to all of the supplementary notes written specifically for this course, organized by topic. These are meant to be supplementary to other resources – other textbooks, lectures, etc. It should also be noted that some of these notes only consist of examples or explain just one specific topic.

These notes are primarily written by Suraj Rampure, with contributions by Fahad Kamran, Hermish Mehta, Jerry Huang, and Sagnik Bhattacharya. While these notes are not actively being maintained, feel free to email suraj.rampure@berkeley.edu if you spot any issues with them. It would also be appreciated if you could fill out this brief survey to let us know the notes have been valuable to you. Thank you!

Set Theory

• Sets and Set Operations
• Functions and Bijections
• Sets of Numbers
• Propositional Logic
• Cheat Sheet

Proof Techniques

• Foundational Proof Techniques
• Mathematical Induction
• Series and Sequences

Number Theory and Modular Arithmetic

• Primality and Divisibility
• Modular Arithmetic

Counting

• Principle of Inclusion-Exclusion
• Key Examples in Counting
• Stars and Bars

Polynomials

• Binomial Theorem
• Vieta’s Formulas
• Representation and Interpolation
• Factor and Remainder Theorems

Miscellaneous

• Sigma and Pi Notation
• Complex Numbers

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