This page shows a rough outline of what will be/was covered in each lecture/discussion section, and dates of tests. Schedule for future lecture topics is tentative, and may change. Roughly the course will cover Logic and Proofs (Chapters 1 and 3), basic mathematics (Chapter 4), Induction (Chapter 5), Arithmetic (Chapter 9), more Induction and Recursion (Chapters 6 and 7), Graphs and Orders (Chapters 10 and 12), and Counting (Chapters 14 and 15), in that order; here chapter references point to the relevant chapters in the textbook. We may also cover Chapters 8, 16, 17, and 18.
Video recording of the lectures will be available through Engineering's Echo360 service. To login, you will need to enter their University of Illinois email address. You will then be prompted to authenticate using their Active Directory (AD) password. Once you’re authenticated, you should see a dashboard page displaying content for which you are enrolled as a student. If need further documentation on how to use this platform, please consult this page.
Video recording of the lectures is also available through Class Transcribe. Class Transcribe automatically close captions the videos, and the resulting videos are also searchable.
In the table below, "MCS" refers to the class textbook, Mathematics for Computer Science. Topics covered in the lecture can often also be found in the alternate textbook for the course Building Blocks for Theoretical Computer Science, which is referred to below as "BBTCS".
Week  Date  Lecture/Test Topic  Reference Material 


Aug 26  Administrivia, and Introduction to Proofs [slides, worksheet, scribbled notes] 
meetings and materials assigned work MCS: Section 1.1 
Aug 28  Propositional Logic [worksheet, scribbled notes] 
MCS: Sections 3.1 to 3.3; BBTCS: 2.1 to 2.9  
Aug29/30  Discussion: Propositional Logic  MCS: 3.1 to 3.3  
Aug 30  Propositional Logic (contd), Satisfiability, Validity [worksheet, scribbled notes] 
MCS: Sections 3.4, 3.5; BBTCS: 2.1 to 2.9 CBTF, CBTF video and reservation, CBTF Documentation 


Sep 02  No class. Labor Day  
Sep 04  Quantifiers and Proofs [worksheet, scribbled notes] 
MCS: Sections 1.1 to 1.5 and 3.6; BBTCS: 3.1 to 3.9  
Sep 05/06  Discussion: Quantifiers and Proofs  MCS: 3.6 and 1.1 to 1.5  
Sep 06  Proofs: Contrapositives and IFF [worksheet, scribbled notes] 
MCS: Sections 1.5 and 1.6; BBTCS: 3.12 and 3.13  

Sep 0810  CBTF Test 1 on Logic  Skill set 
Sep 09  Proofs: By Cases, Contradiction, and Existentials [worksheet, scribbled notes] 
MCS: Sections 1.7 and 1.8; BBTCS: 3.10, 3.11, and 17  
Sep 11  Sets [worksheet, scribbled notes] 
MCS: Section 4.1; BBTCS: 5 Instructions for taking long tests. 

Sep 12/13  Discussion: More Proofs  MCS: 1.5 to 1.9  
Sep 13  Functions, Binary Relations [worksheet, scribbled notes] 
MCS: Sections 4.2 to 4.4; BBTCS: 6,7,8  

Sep 16/17  Long Test 1 on Proofs  Skill set 
Sep 16  No class. Evening test  
Sep 18  Finite Cardinality and Induction [worksheet, scribbled notes] 
MCS: Sections 4.5, Chapter 5; BBTCS: Chapter 11  
Sep 19/20  Discussion: Sets and Functions  MCS: Chapter 4  
Sep 20  Induction [worksheet, scribbled notes] 
MCS: Chapter 5; BBTCS: Chapter 11  

Sep 2224  CBTF Test 2 on Predicate Logic, Sets, Functions, and Relations  Skill set 
Sep 23  Divisibility [worksheet, scribbled notes] 
MCS: Sections 9.1, 9.2, and 9.6; BBTCS: Chapter 4  
Sep 25  Proving Algorithms: Inductive Invariants [worksheet, scribbled notes] 
MCS: Chapter 6, Section 9.2; BBTCS:   
Sep 26/27  Discussion: Induction Proofs  MCS: Chapters 5 and 6  
Sep 27  Modular Arithmetic, and Equivalence relations [worksheet, scribbled notes] 
MCS: Chapter 9, Section 10.10; BBTCS: Chapter 4 and 6  

Sep 30/Oct 01  Long Test 2 on Sets, Functions, Relations, and Induction  Skill set 
Sep 30  No class. Evening test  
Oct 02  Cryptography [worksheet, scribbled notes] 
MCS: Chapter 9; BBTCS:   
Oct 03/04  Discussion: Invariant Principle and Number Theory  MCS: Chapter 9, and Section 10.10  
Oct 04  Recursive Structures and Structural Induction [worksheet, scribbled notes] 
MCS: Sections 7.1 to 7.5; BBTCS: Chapter 12 (?)  

Oct 0608  CBTF Test 3 on Number Theory and the Invariant Principle  Skill set 
Oct 07  Directed Graphs [worksheet, scribbled notes] 
MCS: Sections 10.1 to 10.4; BBTCS: Chapter 10 (?)  
Oct 09  DAGs and Partial Orders [worksheet, scribbled notes] 
MCS: Sections 10.5 to 10.10; BBTCS: Chapter 6 (?)  
Oct 10/11  Discussion: Structural Induction and Directed Graphs  MCS: Sections 7.1 to 7.5 and 10.1 to 10.4  
Oct 11  (Undirected) Graphs [worksheet, scribbled notes] 
MCS: Sections 12.1 to 12.4; BBTCS: 9.1 to 9.4  

Oct 14/15  Long Test 3 on Number Theory, the Invariant Principle, and Structural Induction.  Skill set 
Oct 14  No class. Evening test  
Oct 16  Sub Graphs and Connectivity [worksheet, scribbled notes] 
MCS: Sections 12.7 to 12.9; BBTCS: 9.6 to 9.8, and 9.10  
Oct 17/18  Discussion: Partial Orders and Graphs  Sections from Chapters 10 and 12  
Oct 18  Graph Coloring and Bipartiteness [worksheet, scribbled notes] 
MCS: Section 12.5 and 12.6; BBTCS: 9.11, 10.3  

Oct 2022  CBTF Test 4 on Directed Graphs, DAGs and Partial Orders  Skill set 
Oct 21  Trees [worksheet, scribbled notes] 
MCS: Section 7.6 and 12.11; BBTCS: 13.13, 13.8  
Oct 23  Analysis of Algorithms [worksheet, scribbled notes] 
MCS: Section 14.7; BBTCS: Chapter 14  
Oct 24/25  Discussion: Graphs and Trees  Sections from Chapter 12  
Oct 25  Big Oh [worksheet, scribbled notes] 
MCS: Section 14.7; BBTCS: Chapter 14  

Oct 28/29  Long Test 4 on Directed and Undirected Graphs, and Partial Orders  Skill set 
Oct 28  No class. Evening test  
Oct 30  Summing Series [worksheet, scribbled notes] 
MCS: Section 14.1; BBTCS: Chapter 1(?)  
Oct 31/Nov 01  Discussion: Trees and Asymptotic Analysis  Chapter 12, Section 14.7  
Nov 01  Solving recurrences [worksheet, scribbled notes] 
MCS: Sections 22.1 to 22.3; BBTCS: Chapter 12(?)  

Nov 0305  CBTF Test 5 on Undirected Graphs, Trees, and Big Oh  Skill set 
Nov 04  Analyzing Algorithms: Recursion tree Method [worksheet, scribbled notes] 
Section 1.7 of Jeff's notes; BBTCS: Chapter 15  
Nov 06  Counting: Sums, Products, and Bijection [worksheet, scribbled notes] 
MCS: Sections 15.1 to 15.3; BBTCS: 5.7 to 5.9  
Nov 07/08  Discussion: Summing series and Recurrences  Sections 14.1, 22.1 to 22.3, and Jeff's notes  
Nov 08  Counting: Permutations and Combinations [worksheet, scribbled notes] 
MCS: Section 15.4 to 15.5; BBTCS: 8.4, 8.5  

Nov 11/12  Long Test 5 on Trees, Big O, and Recurrences  Skill set 
Nov 11  No class. Evening test  
Nov 13  Binomial and Multinomial Theorems [worksheet, scribbled notes] 
MCS: Section 15.6 and 15.7; BBTCS: 18.4 to 18.8  
Nov 14/15  Discussion: Counting  Sections 15.1 to 15.7  
Nov 15  Pigeon Hole Principle [worksheet, scribbled notes] 
MCS: Section 15.8; BBTCS: 8.3  

Nov 1719  CBTF Test 6 on Recursion Tree method and Counting  Skill set 
Nov 18  Principle of InclusionExclusion and Combinatorial Proofs [worksheet, scribbled notes] 
MCS: Sections 15.9 and 15.10; BBTCS: Section 5.7  
Nov 20  Probability [worksheet, scribbled notes] 
MCS: Chapter 17  
Nov 21/22  Discussion: Counting II  Sections 15.6 to 15.10  
Nov 22  Conditional Probability [worksheet, scribbled notes] 
MCS: Chapter 18  

Nov 23 to Dec 01  Thanksgiving Break  

Dec 02  Probability Theory: Pitfalls and Paradoxes [worksheet, scribbled notes] 
MCS: Chapters 17 and 18 
Dec 04  Infinite Sets [worksheet, scribbled notes] 
MCS: Section 8.1; BBTCS: Chapter 20  
Dec 05/06  Discussion:Probability and ICES forms  
Dec 06  Computability and ICES forms [worksheet, scribbled notes] 
MCS: Section 8.2; BBTCS: Chapter 20  

Dec 09/10  Long Test 6 on Recursion Tree Method, Counting, and Probability  Skill set 
Dec 09  No class. Evening test  
Dec 11  Course Review 