Math 10B: Methods of Mathematics
UC Berkeley | Summer 2016
LEC 001/DIS 101: MTWTF 11 AM - 1 PM in 736 Evans Hall
Instructor: Theodore Zhu
Email:
Office: 840 Evans Hall
Office Hours: M 2-3, W 10-11, Th 2-3
Course Description
Elementary combinatorics and discrete probability theory. Introduction to graphs, matrix algebra, linear equations, difference equations, and differential equations.
Textbook
The main reference is the four-part series of notes available on bCourses:
Combinatorics, Discrete Probability, Dynamics, Matrix Algebra
Exams
Homework
There are 12 homework assignments. Homework is typically due on Tuesdays and Fridays at the beginning of class. Collaboration is welcome and encouraged, but each student must turn in his or her own assignment. At the end of the semester, the lowest homework score for each student will be dropped.
- Homework 1 due Friday, June 24. Solutions
- Homework 2 due Tuesday, June 28. Solutions
- Homework 3 due Friday, July 1. Solutions
- Homework 4 due Tuesday, July 12. Solutions
- Homework 5 due Friday, July 15. Solutions
- Homework 6 due Tuesday, July 19. Solutions
- Homework 7 due Friday, July 22. Solutions
- Homework 8 due Thursday, July 28 Solutions
- Homework 9 due Tuesday, August 2 Solutions
- Homework 10 due Friday, August 5 Solutions
- Homework 11 due Tuesday, August 9 Solutions
- Homework 12 (ungraded) Solutions
Grading
- Course components will be weighted as follows: Homework 15%, Midterms 20% each, Final Exam 45%.
- Important dates: The last day to add or drop this course is Friday, July 1. The last day to change your grading option is Friday, July 29.
- Incomplete grades will be assigned only to students with a documented medical, personal or family emergency prior to completion of the course. Students receiving such grades are required to have been doing work of passing quality up to the intervention of the emergency.
Schedule
- 06/20: Introduction. Basic counting principles. Product rule and sum rule (Combinatorics 5-25)
- 06/21: Inclusion-exclusion. Pigeonhole principle. Basics of functions (Combinatorics 26-46)
- 06/22: Permutations and combinations. Binomial coefficients and binomial theorem (Combinatorics 47-74)
- 06/23: Balls and boxes. Bars and stars (Combinatorics 75-106)
- 06/24: Discrete probability. Uniform probability spaces (Discrete Probability 4-23)
- 06/27: Conditional Probability. Bayes' rule
- 06/28: Independence of events
- 06/29: Random variables
- 06/30: Discrete distributions
- 07/01: Expectation of random variables
- 07/05: Review
- 07/06: First Midterm Exam
- 07/07: Go over exam
- 07/08: Derivation of expected values of basic discrete distributions
- 07/11: Techniques for computing expected value. Variance of random variables
- 07/12: Derivation of variance of basic discrete distributions
- 07/13: Sampling and estimation. Confidence intervals
- 07/14: Hypothesis testing. Chi-squared tests
- 07/15: Sequences. Recurrence relations
- 07/18: Solving linear homogeneous constant-coefficient recurrence relations
- 07/19: Nonhomogeneous reccurence relations. Differential equations
- 07/20: Constant-coefficient linear ODE. Linear first-order ODE
- 07/21: Separable ODE. Partial fractions
- 07/22: Review and practice of ODE
- 07/25: More on differential equations. Basic of matrices
- 07/26: Matrix algebra
- 07/27: Review
- 07/28: Review
- 07/29: Second Midterm Exam
- 08/01: Go over exam. Review matrix algebra
- 08/02: Determinants and inverses
- 08/03: Gaussian elimination. Computing inverses of square matrices
- 08/04: Eigenvalues and eigenvectors
- 08/05: Applications of eigenvalues and eigenvectors. Diagonalization
- 08/08: Least squares and linear regression
- 08/09: Dynamic programming
- 08/10: Review
- 08/11: Review
- 08/12: Final Exam
Links
bCourses
Past Exams
Math 10B Spring 2016
Student Learning Center