Mathematics (MA)
A practical study of the skills and tools needed to work with quantitative information from the real world. Students will learn and explore mathematical concepts such as arithmetic, fractions, decimals, percentages, descriptive statistics and basic probability, estimation, unit analysis, absolute and relative change, and linear and exponential growth. Students will also represent and interpret numerical data in tabular and graphical forms. Material will be applied to a wide variety of fields.
In many areas of the social and management sciences, mathematics can be used to make predictions, help allocate scarce resources, maximize profits, make policy decisions, and so on. This use of mathematics is called mathematical modeling. In this course we investigate a variety of scenarios which can arise in the "real world" where math modeling can come into play, and we learn about some of the most important techniques of math modeling such as linear programming, probability theory, statistical techniques, integer programming, and Markov chains.
Provides students with an opportunity to study interdisciplinary problems through a quantitative lens. During the course, students will build models, analyze and interpret results using traditional mathematics and computer-based simulations, and present their findings in both written and oral presentations. Students will explore problems from many disciplines including ecology, biology, finance, and epidemiology. Modeling techniques studied in this course include discrete dynamical systems and stochastic models.
An introductory course for liberal arts and education majors or anyone seeking a general, nontechnical overview of mathematics. Topics covered include set theory, review of number systems, geometry concepts, basic concerns of probability and statistics, and introductory number theory.
An introduction to derivatives, integrals, and their applications. Primarily for students who are not adequately prepared for MA 111, this course (together with MA 109) covers the same material as MA 111 but integrates the material requisite to calculus with the calculus itself. Note that MA 108 alone cannot be used as a substitute for MA 111. Successful completion of MA 108 and MA 109 is equivalent to completion of MA 111.
A continuation of MA 108. A study of exponential, logarithmic, and trigonometric functions and their applications in differential and integral calculus. Successful completion of MA 108 and MA 109 is equivalent to completion of MA 111.
A detailed study of the mathematical tools necessary for success in calculus and statistics courses. Students will build their quantitative reasoning skills, with a particular focus on understanding functions and covarying quantities. These skills include creating, refining, and algebraically manipulating models involving polynomials, rational functions, exponentials, logarithms, and trigonometric functions. Students will relate these models to real-life applications and analyze them from symbolic, graphical, and numerical perspectives.
Derivatives, integrals and their applications. Techniques of differentiation. Integration and differentiation of exponential, logarithmic and trigonometric functions.
An exploration of integral calculus. Topics include techniques of integration, applications of integration, and improper integrals.
An exploration of integral calculus. Topics include techniques of integration, applications of integration, and improper integrals.
An exploration of infinite sequences and series. Topics include geometric series, convergence tests, Taylor series, and power series.
An examination of how mathematical ideas are embodied in the visual arts, architecture, and design, and how the arts have helped shaped advances in math and computer science. From ancient Greek art to the Renaissance, and from Islamic patterns to contemporary computer-generated art, math has an important place in the world of art, architecture, and design both within museum spaces and all around us. Students will explore these relationships in the context of mathematical concepts such as geometry, proportion, basic statistics, measurements, and common functions by studying original works of art and actively engaging with these mathematical concepts through hands on exercises in Skidmore's Tang Teaching Museum.
Introductory level. Students will work collaboratively on problems posed in various undergraduate mathematics journals and other sources. Solutions to journal problems will be submitted to the journal editors for acknowledgment and possible publication. Problems are taken from all areas of specialty within mathematics.
Introductory level. Students will work collaboratively on problems posed in various undergraduate mathematics journals and other sources. Solutions to journal problems will be submitted to the journal editors for acknowledgment and possible publication. Problems are taken from all areas of specialty within mathematics.
Introductory level. Students will work collaboratively on problems posed in various undergraduate mathematics journals and other sources. Solutions to journal problems will be submitted to the journal editors for acknowledgment and possible publication. Problems are taken from all areas of specialty within mathematics.
Vector spaces, matrices and linear transformations, determinants, solution of linear equations.
Multivariable calculus. Topics include vector functions, partial derivatives, multiple integrals, vector fields, and line integrals.
Elementary probability, discrete and continuous random variables, theory of expectation, analysis of distribution functions.
An exploration of multivariable calculus. Topics include parametric equations, polar coordinates, conic sections, vector functions, partial derivatives, and gradients.
Multivariable calculus. Topics include vector functions, partial derivatives, multiple integrals, vector fields, line integrals, surface integrals, vector calculus, divergence and curl.
Topics in classical and modern number theory including congruences, Diophantine equations, quadratic residues.
An introduction to mathematical proof and concepts of abstract mathematics. This course serves as the gateway to the mathematics major. Students will learn to think critically, creatively, and inquisitively about mathematics. They will gain proficiency in foundational areas of formal mathematics, including elementary logic, methods of proof, set theory, functions, and relations. Particular attention will be paid to building students' skills in reading, writing, and revising mathematical arguments.
Intermediate level. Students will work collaboratively on problems posed in various undergraduate mathematics journals and other sources. Solutions to journal problems will be submitted to the journal editors for acknowledgment and possible publication. Problems are taken from all areas of specialty within mathematics.
Intermediate level. Students will work collaboratively on problems posed in various undergraduate mathematics journals and other sources. Solutions to journal problems will be submitted to the journal editors for acknowledgment and possible publication. Problems are taken from all areas of specialty within mathematics.
Intermediate level. Students will work collaboratively on problems posed in various undergraduate mathematics journals and other sources. Solutions to journal problems will be submitted to the journal editors for acknowledgment and possible publication. Problems are taken from all areas of specialty within mathematics.
Topics that complement the established lower level course offerings in mathematics will be selected. Emphasis will be on the nature of mathematical thought.
An introduction to the theory and applications of differential equations.
Exploration of a research topic in mathematics. The students, in collaboration with a faculty mentor, will participate in a research project in a particular area of mathematics which may be related to the faculty member's research program.
An introduction to the theory and applications of graphs. Topics may include graphs and digraphs, connectivity, trees, Euler and Hamiltonian cycles, and graph embeddings.
Rigorous treatment of foundational issues in analysis. Topics may include set theory, the real number system, sequences, series, limits and continuity, theory of differentiation and integration, and elementary notions of topology.
An introduction to the theory of probability and applications of probability in modeling real world phenomena. The goal of this course is to introduce students to the language, ideas, and tools of probability, the science of uncertainty. Probabilistic concepts, derivations, and problem solving are emphasized. Computational tools will also be used to explore and verify theoretical results. Topics include counting methods, random variables, discrete and continuous distributions, mathematical expectation, functions of random variables, joint distributions, and limit theorems.
Study of various topics in modern geometry, with emphasis on the axiomatic method.
Study of the development of mathematical ideas.
An introduction to differential geometry in a classical setting: the study of n-surfaces, embedded in Euclidean space.
Selected topics in topology such as metric spaces, point set topology of Euclidean spaces, introduction to algebraic topology.
An introduction to using computation to obtain approximate solutions to mathematical problems. A variety of algorithms are studied, as are the limitations of using computational methods. Topics include algorithms for solving equations, systems, and differential equations; approximating functions and integrals; curve fitting; round-off errors, and convergence of algorithms.
Survey of algebraic structures; groups, rings, fields, vector spaces, and linear transformations.
Selected topics in advanced algebra.
Selected topics in real analysis.
Analytic functions, complex integration, complex sequences and series, and conformal mapping.
Advanced level. Students will work collaboratively on problems posed in various undergraduate mathematics journals and other sources. Solutions to journal problems will be submitted to the journal editors for acknowledgment and possible publication. Problems are taken from all areas of specialty within mathematics.
Advanced level. Students will work collaboratively on problems posed in various undergraduate mathematics journals and other sources. Solutions to journal problems will be submitted to the journal editors for acknowledgment and possible publication. Problems are taken from all areas of specialty within mathematics.
Advanced level. Students will work collaboratively on problems posed in various undergraduate mathematics journals and other sources. Solutions to journal problems will be submitted to the journal editors for acknowledgment and possible publication. Problems are taken from all areas of specialty within mathematics.
A study of dynamical systems and their application. Topics covered include first-order equations, bifurcation theory, linear systems, phase plane analysis, and chaos. Examples will be considered from problems in medicine and the natural and social science.
Topics that complement the established upper level course offerings in mathematics will be selected. Emphasis will be on the nature of mathematical thought.
Special study in mathematics outside the regular department offerings.
Research, discussion, and presentation of selected topics at an advanced level, to provide a capstone experience for the mathematics major; primarily intended for seniors. Senior Seminar in Mathematics - Research, discussion, and presentation of selected topics at an advanced level, to provide a capstone experience for the mathematics major; primarily intended for seniors.
Optional for mathematics majors. Recommended for those working toward professional careers or graduate study in mathematics, and required for those seeking to satisfy the criteria for departmental honors.
Optional for mathematics majors. Recommended for those working toward professional careers or graduate study in mathematics, and required for those seeking to satisfy the criteria for departmental honors.
Professional experience at an advanced level for juniors and seniors with substantial academic experience in mathematics. With faculty sponsorship and departmental approval, students may extend their educational experience in pure or applied mathematics. This course may not be used to satisfy the requirements of any major or minor in the department.