## 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