Mathematics for Computer Science
Lecture Notes
|
SES # |
TOPICS |
|
L1 |
Logic and Sets (PDF) |
|
L2 |
Proofs (PDF) |
|
L3 |
Induction I (PDF) |
|
L4 |
Induction II (PDF) |
|
L5 |
Induction III (PDF) |
|
L6 |
Number Theory I (PDF) |
|
L7 |
Number Theory II (PDF) |
|
L8 |
Graphs I (PDF) |
|
L9 |
Graphs II (PDF) |
|
L10 |
Summations (PDF) |
|
L11 |
Approximations, Asymptotics (PDF) |
|
L12 |
Recurrences (PDF) |
|
L13 |
Counting I (PDF) |
|
L14 |
Counting II (PDF) |
|
L15 |
Counting III (PDF) |
|
L16 |
Generating Functions (PDF) |
|
L17 |
Probability (PDF) |
|
L18 |
Conditional Probability (PDF) |
|
L19 |
Independence (PDF) |
|
L20 |
Random Variables and Distributions (PDF) |
|
L21 |
Expectation I (PDF) |
|
L22 |
Expectation II (PDF) |
|
L23 |
Random Walks (PDF) |
|
L24 |
Special Topics (PDF) |
Recitations
This course has two recitations each week. These recitation sessions emphasize concepts from the lectures and focus on solving problems in small groups. In-class participation during the recitation sessions counts for 20% of a student's grade. The grade is based mainly on the degree of active, prepared participation in the small group, rather than problem-solving success.
|
SES # |
TOPICS |
|
R1 |
Logic (PDF) |
|
R2 |
Case Analysis (PDF) |
|
R3 |
Induction (PDF) |
|
R4 |
Strong Induction (PDF) |
|
R5 |
Well-ordering Principle (PDF) |
|
R6 |
The Pulverizer (PDF) |
|
R7 |
RSA (PDF) |
|
R8 |
Graphs and Trees (PDF) |
|
R9 |
Bipartite Graphs (PDF) |
|
R10 |
Sums and Approximations (PDF) |
|
R11 |
The Quest (PDF) |
|
R12 |
Solving Linear Recurrences (PDF) |
|
R13 |
Basic Counting Notions (PDF) |
|
R14 |
Counting Rules (PDF) |
|
R15 |
Counting (PDF) |
|
R16 |
Generating Functions and Expressions (PDF) |
|
R17 |
The Four-Step Method (PDF) |
|
R18 |
Law of Total Probability (PDF) |
|
R19 |
Probability (PDF) |
|
R20 |
Random Variables, Distributions, etc. (PDF) |
|
R21 |
Expected Value (PDF) |
|
R22 |
Conditional and Total Expectation (PDF) |
|
R23 |
Stencil the Flea (PDF) |
Assignments
This section provides the weekly problem sets for the course.
Problem Set 1 Questions and Solutions (PDF)
Problem Set 2 Questions and Solutions (PDF)
Problem Set 3 Questions and Solutions (PDF)
Problem Set 4 Questions and Solutions (PDF)
Problem Set 5 Questions and Solutions (PDF)
Problem Set 6 Questions and Solutions (PDF)
Problem Set 7 Questions and Solutions (PDF)
Problem Set 8 Questions and Solutions (PDF)
Problem Set 9 Questions and Solutions (PDF)
Problem Set 10 Questions and Solutions (PDF)
Problem Set 11 Questions and Solutions (PDF)
Exams
This section provides examples of the 2-hour quizzes and 3 hour final exam for the course.
Quiz 1 (PDF)
Quiz 2 (PDF)
Final Exam (PDF)