Math 10B

Math 10B - Methods of Mathematics: Calculus, Statistics and Combinatorics -- [4 units]

Course Format: Three hours of lecture and three hours of discussion per week.

Prerequisites: Math 10A or Math 1A.

Description: The sequence Math 10A,B is intended for majors in the life sciences. Elementary combinatorics and discrete and continuous probability theory.  Representation of data, statistical models and testing. (S)

Credit Restrictions: None

Required Textbook: Biocalculus: Calculus, Probability, and Statistics for the Life Sciences (custom UC Berkeley Edition).

Online Class Notes: The Mathematics Department has created extensive online lecture notes for this class, and these will serve as the supplementary text.

Outline of the Course:

Week 1: Basics of counting, inclusion-exclusion

Week 2: Permutations and combinations, binomial coefficients

Week 3: Enumeration techniques

Week 4: Probability spaces and conditional probability

Week 5: Bayes' theorem, independence of events, random variables

Week 6: Discrete probability distributions

Week 7: Expected value, covariance and IIDRV's

Week 8: Limit theorems, continuous random variables

Week 9: PDF's and CDF's. Median, mean and applications

Week 10: Normal distributions, sampling and statistics, estimators and confidence intervals

Week 11: Maximum likelihood method

Week 12: Hypothesis testing: One measurement, large samples, small samples

Week 13: Hypothesis testing: chi^2 goodness of fit, chi^2 independence