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Lecture: Wednesdays, 6:308:00 PM, LeConte 3
Discussion: Mondays, 6:308:00 PM, LeConte 3
Office Hours: Tuesdays 23PM and Thursdays 56PM, Cory 299
Piazza: http://piazza.com/berkeley/fall2018/cs198087
Gradescope: 9XVEPJ
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 higherlevel 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.
A textbook is being written specifically for this course. It is available for free at book.imtdecal.org. There will also be lecture videos embedded into the textbook; this is still a work in progress.
Each "week" in this course starts on a Wednesday (with the exception of the final week). This is because the material presented in lecture on Wednesday is covered in the following Monday's discussion.
Week  Lecture (W)  Discussion (M)  Topic  Homework  
1  Sept. 5  Sept. 10  Course Overview, Intro to Set Theory, Functions Why does this class exist? Overview of the topics covered throughout the course. Definition of a set. Set operations. A general definition of functions. Domain, range. Reading: 1.1, 1.2 Slides Video 
HW 1 Solutions 

2  Sept. 12  Sept. 17  Bijections, Number Sets, Propositional Logic Bijections. Construction of natural numbers, integers, rationals, reals and complex numbers. Introduction to propositional logic. Reading: 1.3, 1.4 Slides (9/12) Slides (9/17) Video 
HW 2 Solutions 

3  Sept. 19  Sept. 24  Proof Techniques Presentation of various proof techniques, and examples of each. How to read proofs. Faulty proofs. Reading: 2.1 Slides Video 
HW 3 Solutions 

4  Sept. 26  Oct. 1  Proof Techniques, Continued Analysis of proof techniques, continued. Mathematical induction. Reading: 2.2 Slides Video 
HW 4 Solutions 

5  Oct. 3  Oct. 8  Midterm Review Note: This week's homework is not to be submitted, rather it is meant to be preparation for the upcoming midterm. Slides Video 
HW 5 Solutions 

6  Oct. 10  Oct. 15  Midterm Inclass midterm on October 10th. Discussion on October 15th will be taking up midterm. Exam Solutions 

7  Oct. 17  Oct. 22  Number Theory Division algorithm. Introduction to modular arithmetic. Slides Video Slides (10/22) Video (10/22) 
HW 6 Solutions 

8  Oct. 24  Oct. 29  Counting Thinking about the "number of ways" to do something. Permutations and combinations. Stars and bars. Principle of InclusionExclusion. Slides Slides (10/29) Video (10/29) 
HW 7 Solutions 

9  Oct. 31  Nov. 5  Pascal's Triangle, Combinatorial Proofs, Binomial Theorem Properties of Pascal's triangle. Combinatorial proofs. Introduction to the binomial theorem. Slides Video 
HW 8 Solutions 

10  Nov. 7  N/A (Veteran's Day)  Vieta's Formulas Vieta's formulas for polynomials of degree 2, 3, 4. Generalized Vieta's. Examples. Slides Video 
HW 9 (11/14) 

11  Nov. 14  Nov. 19  Polynomial Interpolation, with Modular Arithmetic Lagrange Interpolation. Lagrange Interpolation under modular arithmetic. Notebook (html) Notebook (ipynb) 
HW 10 Solutions 

12  N/A (Thanksgiving)  Nov. 26  Final Review No class Wednesday of Thanksgiving. Inclass final review Monday, Nov. 26. 

13  Nov. 28  N/A  Final In class final on Wednesday, November 28th. Exam Solutions 
Extra Credit 
The course will be offered for 2 units, P/NP. There will be one 1.5h lecture each Wednesday, and one 1.5h discussion each Monday.
There will be weekly problem sets, which are released on Wednesdays after lecture and due the following Monday at 6:30PM, at the start of discussion. Problem sets are graded on effort. The problem set will be taken up in that Monday's discussion section; the idea is that students will discuss amongst each other their approaches to the problems, and the staff will facilitate this discussion.
Your grade in this course is calculated on a 100point scale.
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Edward Im (edwardim@berkeley.edu) Hi! I'm a thirdyear studying Economics and Computer Science. I love math, and I hope to help you love it too. In my free time, I love running, overeating, and singing in the shower (ask my roommates!) 

Ziv Lotzky (zivlotzky@berkeley.edu) Hey I’m Ziv! I’m a senior math major originally from New York (go yankees!). I love logic puzzles, riddles, and quantitative finance. 

Josh Geng (joshgeng@berkeley.edu) I'm a second year Statistics and Econ major from Calgary, Canada. I did math competitions for the majority of my life and I was able to travel the world because if it. Come to RSF after discussion to get swole with me! 