Mathematics and Statistics Program

Introduces statistics majors to econometric methods for analyzing time series data, building

on regression foundations. Covers OLS assumptions and diagnostics, heteroscedasticity, autocorrelation, distributed

lag and dynamic models, stationarity testing, ARIMA, VAR models, Granger causality, cointegration, error correction

models, and ARCH/GARCH models for volatility, with applications to real economic and financial data using Stata

Techniques of Integration
Improper Integrals
Sequences
Series of Constant Terms
Power Series
Differential Calculus of Functions of Several Variables
Double Integrals

Real Number Systems
Algebraic Expressions
One- and Two-Dimensional Coordinate Systems
Functions
Equations
Inequalities
Word Problems
Variations

Real Number Systems, Algebraic Expressions, One- and Two-Dimensional Coordinate Systems, Functions, Equations and Inequalities, Word Problems and Variations

presentation of data; frequency distributions; measures of central tendency; measures of dispersion; probability distributions; statistical inference; correlation and regression

Presentation of data; frequency distributions; measures of central tendency; measures of dispersion; probability distributions; statistical inference; correlation and regression

MATH 40 is an introduction to calculus and its applications in the life sciences. Rather than focusing only on mathematical techniques, we will explore how calculus can be used to describe, analyze, and understand phenomena in biology and other life-science disciplines.

Throughout the course, we will encounter concepts such as limits, derivatives, integrals, and differential equations and see how these ideas can help us model and interpret real-world situations involving population growth, rates of change, biological processes, and other applications in the life sciences.

This course covers the notions on limits, continuity, derivatives and their applications, differentials, antiderivatives, definite integrals, and its application. It gives students appreciations of how complex real-world problems can be solved through different tools of calculus such as limits, differentiation, and integration.

Graph characterization and operations
graphs and algorithms
trees
connectivity
traversability
matching
factorization
planarity
colorability
digraphs and tournaments
binomial and multinomial coefficients
pigeonhole principle and Ramsey numbers
the principle of inclusion and exclusion
generating functions
recurrence relations

Basic concepts
problem formulation
graphical solution for two-variable problems
simplex algorithm and other algorithms for special LP problems
duality
sensitivity analysis

Binary operations, algebraic systems such as semigroups, rings, integral domains, fields, extensions