This course is a calculus-based introduction to probability, with applications. The course begins with an quick treatment of basic probability, and then moves on to apply more sophisticated mathematical techniques (e.g., generating functions and tools from calculus) to probability models of various kinds, with applications. There is fairly thorough coverage of the central limit theorem, though not with complete proofs. The course concludes with a section on Markov chains and random walks.
No prior knowledge of probability will be assumed. The course occasionally uses topics from multivariable calculus (e.g., multiple integrals), and so Math 121 or Math 216 is a prerequisite. This may be waived for students whose background is strong, especially those who have some background in probability or statistics.
Math 218 is a very useful and practical course for math majors, but is not intended solely for majors. Applications and examples will play a very important role, and students majoring in other sciences and social sciences (e.g., economics and psychology) may also find this material relevant and useful. Math 218 is a prerequisite for Mathematical Statistics, taught at the 300-level.
Prerequisites:
Math 121 or Math 216 (Multivariable
Calculus/Advanced Calculus) or consent of instructor.
Who should take this course?
Math majors looking for a 200-level elective
Biology majors interested in genomics
Anyone seeking a deeper understanding of statistics or probabilistic modeling
Anyone interested in random walks
Anyone interested in games of chance
Anyone looking for an intermediate-level math course with extensive applications
Topics covered:
Axioms for discrete and continuous probability spaces
Classical dice, card, and coin tossing problems
Elementary combinatorics of permutations and combinations
Conditional probability and Bayes' Law
Random variables, expected value and variance
Fundamental probability models: binomial, Poisson, geometric, hypergeometric, exponential,
Gaussian
Generating functions
The laws of large numbers and central limit theorem (emphasis on statements, not proofs)
Examples from statistics
Random walks
Markov chains
For detailed information about Math 218 this year, please consult the list of Fall Courses and Spring Courses linked to the Mathematics and Statistics Home Page.