Introduction to Mathematical Thinking

CS 198-087 @ UC Berkeley

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Access the notes for this class here.


This course was discontinued after Spring 2019. However, it appears that some students have found the material useful, so we will keep all content public on this site. If you’ve used the material on this site for any reason, please fill out this brief survey to help us understand how this site is being used. Thanks!

Content and Schedule

Week Date Topic Resources Homework
1 Tue. 01/29 Course Overview Slides
Thu. 01/31 Set Theory, Functions Slides
Note: Sets and Set Operations
Note: Functions and Bijections
HW 1
2 Tue. 02/05 Bijections, Number Sets Slides
Note: Sets of Numbers
Thu. 02/07 Number Sets, Propositional Logic Slides
Note: Propositional Logic
HW 2
3 Tue. 02/12 Propositional Logic Slides
Note: Notation Cheat Sheet
Thu. 02/14 Basic Proof Techniques
Quiz 1 in class
Note: Foundational Proof Techniques
HW 3
4 Tue. 02/19 Basic Proof Techniques Slides
Thu. 02/21 Induction Slides
Note: Mathematical Induction
HW 4
5 Tue. 02/26 Strong Induction, Series and Sequences Slides
Thu. 02/28 Series and Sequences
Quiz 2 in class
Note: Series and Sequences
HW 5
6 Tue. 03/05 Division Algorithm and Primality Slides
Note: Primality and Divisibility
Thu. 03/07 Modular Arithmetic Slides
Note: Modular Arithmetic
7 Tue. 03/12 Finding Modular Inverses
(Ani Nrusimha*)
Slides (from Fall 2018)
Video (from Fall 2018)
Thu. 03/14 Review of NT/MA
(Lecture by TAs Adel, Jai, Sagnik)
Quiz 3 online
Refer to Homework 5 solutions
8 Tue. 03/19 Counting
(Ani Nrusimha)
Slides by Ani
Slides (from Fall 2018)
Note: Principle of Inclusion-Exclusion
Note: Key Examples in Counting
Note: Counting (by Jerry Huang)
Thu. 03/21 Counting
(Ani Nrusimha)
Slides by Ani
Video (from Fall 2018)
Note: Stars and Bars
HW 6
9 Tue. 03/26 No Class (Spring Break)
Thu. 03/28 No Class (Spring Break)
10 Tue. 04/02 Counting Review Slides
Thu. 04/04 Counting Review, Combinatorial Proofs Slides
11 Tue. 04/09 Binomial Theorem
Quiz 4 in class
Note: Binomial Theorem
Thu. 04/11 Binomial Theorem, Vieta’s Formulas Slides
Note: Vieta’s Formulas
HW 7
12 Tue. 04/16 Vieta’s Formulas Slides
Thu. 04/18 No Class
13 Tue. 04/23 Review Slides
HW 8
Thu. 04/25 Review Slides
14 Tue. 04/30 Quiz 5 in class
Thu. 05/02 Probability, Closing Thoughts Slides
Extra Credit

* Ani Nrusimha,, will be covering these lectures. Feel free to reach out to him with any questions.

Spring 2019 quizzes:

From previous semesters:

Additional resources:


Berkeley’s highly theoretical Computer Science curriculum demands a high level of mathematical maturity. While those with extracurricular math experience from high school are familiar with dense notation, complex mathematical objects, and proof techniques, many students find foundational courses like CS 70, CS 170, and Math 55 confusing and inaccessible.

Introduction to Mathematical Thinking bridges the gap. We teach mathematical maturity. Our curriculum exposes students to familiar concepts in a more precise, generalized way. By the end of our course, students will be able to:

As a result, this course will prepare students for higher-level mathematics courses, such as CS 70 at Berkeley. However, students can enroll in the course even if they aren’t planning on taking these courses or are not in CS/EECS; these skills and concepts are highly transferrable.

There are no prerequisites for this course. We’re working really hard to make the material accessible for all backgrounds.

Disclaimer: This course is not a prerequisite for CS 70, nor is it affiliated with the CS 70 instructors or course staff in any way. The official prerequisites for CS 70 are specified in the course description. CS 70 staff makes no guarantees regarding the material covered in this course.


The course will be offered for 2 units, P/NP.

There will be weekly problem sets, which are graded on effort, not correctness. Attendance is mandatory, and NPs will be given to students who have more than 3 unexcused absenses.

The course is graded on a 100 point scale:

A passing grade will be given to students with 65 points or more (note the new threshold). We reserve the right to change this threshold, but we would only decrease it (i.e. we will not make it any harder to pass).

Frequently Asked Questions


For all course related communications, please email


Suraj Rampure (

Hey, I’m a third year EECS major from Windsor, Ontario (right across the border from Detroit). I like cars, tech, teaching and rooting for LeBron (go Cavs Lakers!). This is my second semester teaching this course, fifth semester as a part of CSM, and fourth semester as a GSI; currently, I’m TA’ing Data 100, but have TA’d CS 61A and Data 8 in the past. I’m super excited that this course is finally a reality, and I’m hoping you are as well.

Teaching Assistants

Jai Bansal (

Hey everyone! This is my first year at Cal hoping to major in CS and Applied Mathematics. In my free time, I love playing Ultimate Frisbee and watching basketball, football, soccer (or any sport you can name) and listening to way too much Logic. Feel free to talk to me about anything! Excited to TA for the first time!

Sagnik Bhattacharya (

I’m a CS and stats-intended freshman. You can find me running on the streets of Berkeley when I’m not biking between classes or trying to hack the mainframe. Talk math and computers (and environmental science!) to me.

Alexia Colmenero (

I am a sophomore Computer Science major from San Diego. I am a gemini who likes video games, and is excited to work on this course! I use they/them pronouns.

Divya Mohan (

Heya! I’m a sophomore EECS major, originally from the Bay Area (specifically, Belmont). I am also meme trash; find me on UCBMFET any day, all day. I’m interested in data science, and I love helping my peers :)

Adel Setoodehnia (

Hello! I’m Adel, a third-year Mathematics and Computer Science student from Union, New Jersey. When I have free time you could probably find me playing soccer, listening to music, playing guitar, chilling with a book, or cooking/eating all types of good food. Looking forward to meeting you all!