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