39 courses with the subject MATH, each shown exactly as we captured it from the college's catalog, with every element we hold. Where the wording looks broken, that is our reading of the catalog, not the college's text.
MATH 117Gateways to Mathematics
This course explores the nature of mathematics and its role in contemporary society. The content and format of the course vary depending on the instructor's interests. In particular, the course may focus on one or two mathematical topics in depth or survey a wider range of topics. Recent topics have included mathematics of voting, probability, game theory, finance, and connections between mathematics and the arts. Offered periodically.
This course combines a full semester of differential calculus with reviews of algebra and pre-calculus topics for students who did not complete a pre-calculus course in high school, or are otherwise not prepared to enroll in MATH 120. Review of algebraic techniques and the language of functions are integrated with topics from the calculus of functions of a single real variable, including trigonometric, exponential, and logarithmic functions. Topics are explored graphically, symbolically, and numerically. Class meets four times per week, including one laboratory meeting. Credit may be earned for either MATH 119 or MATH 120, but not both. Offered in the fall semester. Prerequisite: mathematics placement recommendation. OLE Core Requirement: Quantitative and Computational Reasoning.
This course introduces differential and integral calculus of functions of a single real variable, including trigonometric, exponential, and logarithmic functions. Derivatives, integrals, and differential equations are explored graphically, symbolically, and numerically. Applications of these topics are emphasized throughout the course. Credit may be earned for either MATH 119 or MATH 120, but not both. Students may not enroll in this course if they have AP, IB, or CAL Calculus I credit. Offered each semester and during January term. Prerequisite: mathematics placement recommendation. OLE Core Requirement: Quantitative and Computational Reasoning.
This course covers methods and applications of integration, geometric and Taylor series, and introduces partial derivatives and double integrals. Credit may be earned for either MATH 126 or MATH 128, but not both. Offered each semester. Prerequisite: MATH 119 or MATH 120 or equivalent, or mathematics placement recommendation. OLE Core Requirement: Quantitative and Computational Reasoning.
This course covers the material in MATH 126 in greater depth and breadth. Credit may be earned for either MATH 126 or MATH 128, but not both. Offered annually in the fall semester. Prerequisite: 4 or 5 on AP Calculus AB exam or permission of the Mathematics Placement Director. OLE Core Requirement: Quantitative and Computational Reasoning.
This course beautifully illustrates the nature of mathematics as a blend of technique, theory, abstraction, and applications. The important problem of solving systems of linear equations leads to the study of matrix algebra, determinants, vector spaces, bases and dimension, linear transformations, and eigenvalues. Offered each semester and during January term. Prerequisite: MATH 119, MATH 120 or CSCI 221, or with permission of the Mathematics Placement Director. OLE Core Requirement: Quantitative and Computational Reasoning.
This course extends important ideas of single-variable calculus (derivatives, integrals, graphs, approximation, optimization, fundamental theorems, etc.) to higher-dimensional settings. These extensions make calculus tools far more powerful in modeling the (multi-dimensional) real world. Topics include partial derivatives, multiple integrals, transformations, Jacobians, line and surface integrals, and the fundamental theorems of Green, Stokes, and Gauss. Offered each semester. Prerequisites: MATH 126 or MATH 128, and MATH 220.
This course introduces differential equations and analytical, numerical, and graphical techniques for the analysis of their solutions. First- and second-order differential equations and linear systems are studied. Applications are selected from areas such as biology, chemistry, economics, ecology, and physics. Laplace transforms or nonlinear systems may be covered as time permits. Students use computers extensively to calculate and visualize results. Offered each semester. Prerequisite: MATH 126 or MATH 128 and MATH 220.
In this course students use topics in discrete mathematics to engage in problem solving, abstract mathematical thinking, and logical reasoning. Students practice proof writing in multiple contexts, including propositional and predicate logic; the foundations of set theory, functions, and relations; elementary number theory; arithmetic and geometric progressions; permutations, combinations, and basic probability; and graph theory. Offered most semesters. May not be taken after MATH 244 or MATH 252, except with instructor permission. Prerequisite: CSCI 221, MATH 126 or MATH 128.
MATH 235Discrete Mathematical Reasoning in Budapest (study abroad)
In this course students use topics in discrete mathematics to engage in problem solving, abstract mathematical thinking, and proof writing. Topics include logic, set theory, functions, and relations; elementary number theory; arithmetic and geometric progressions and graph theory. Also counts toward the computer science major and business and management studies concentrations. Prerequisite: MATH 126 or MATH 128 or CSCI 221.
This course introduces students to the essential modeling techniques of formulation, implementation, validation, and analysis. Students engage in these areas by combining experiment, mathematical theory, statistics, and computation to better understand a wide variety of biological systems. Offered annually in the spring semester. Prerequisite: MATH 126 or MATH 128, and familiarity with R programming (BIO 150 or SDS 172 or CSCI 125 or equivalent programming experience). OLE Core Requirement: Natural Science.
This course introduces the study of patterns and relationships satisfied by natural numbers. Topics include divisibility, modular arithmetic, prime numbers, congruences, primitive roots, and quadratic residues. The course is offered in Budapest, Hungary, a world center for mathematics research. The course includes several hours of Hungarian language instruction and lectures by Hungarian mathematicians and scholars. Offered annually during January Term. Prerequisite: MATH 220 or permission of instructor.
Modern mathematics is characterized by the interaction of theoretical and computational techniques. In this course, students study topics from pure and applied mathematics with the aid of computation. Symbolic, graphical, and numerical computational techniques are introduced. Students develop computational skills sufficient to investigate mathematical questions independently. No previous programming experience is required. Offered annually. Prerequisite: MATH 220.
Students encounter the theory of calculus and develop tools for communicating mathematical ideas with technical accuracy and sophistication. The goal is mastery of the concepts (e.g., limit, continuity, derivatives, and integrals) necessary to verify such important results as the Fundamental Theorem of Calculus, the Mean Value Theorem, and the Bolzano-Weierstrass Theorem. Emphasis is on theory and on developing the ability to write proofs. Offered each semester. Prerequisite: MATH 126 or MATH 128, and MATH 220. Permission of instructor required for first-year students. OLE Core Requirement: Writing Across the Curriculum.
Algebra is concerned with sets of objects and operations that satisfy a few basic properties. Using the properties we study axiomatic systems such as groups, rings, and fields, covering topics such as homomorphisms, cosets, quotient structures, polynomial rings, and finite fields. Emphasis is on theory and on developing the ability to write proofs. Offered each semester. Prerequisite: MATH 220. Permission of instructor required for first-year students. OLE Core Requirement: Writing Across the Curriculum.
MATH 257Noether and Kovalevskaya: Algebra/Analysis/Access in Europe (abroad)
Students study the mathematics of Emmy Noether and Sonya Kovalevskaya, visit cultural and historical sites in Germany and Sweden associated with the women, and learn about the societal contexts in which they lived and worked. Noether was fundamental in the development of algebra, in particular the theory of how rings decompose into ideals. Kovalevskaya extended work of Cauchy to prove the main theorem for analytic solutions to partial differential equations. Offered alternate years during January Term. Apply through Smith Center for Global Engagement. Prerequisites: MATH 252, or MATH 230 and MATH 244. OLE Core Requirement: OLE Experience in Practice.
Computational geometry is the study of algorithms for solving geometric problems. This course introduces students to concepts of discrete geometry and their use in geometric algorithms. Topics may include polygons and polyhedra, triangulations, convex hulls, Voronoi diagrams, and configuration spaces. This course combines both theoretical and computational perspectives, and offers applications to areas such as computer graphics, mesh generation, robotics, and geographic information systems. Offered alternate years during January term. Prerequisites: MATH 242 or MATH 244 or MATH 252 or (MATH 234 and CSCI 221), or instructor permission.
This course introduces the mathematics of randomness. Topics include probabilities on discrete and continuous sample spaces, conditional probability and Bayes' Theorem, random variables, expectation and variance, distributions (including binomial, Poisson, geometric, normal, exponential, and gamma) and the Central Limit Theorem. Students use computers to explore these topics. Offered each semester. Prerequisite: MATH 126 or MATH 128.
recommendation. Students are introduced to modeling and mathematical optimization techniques (e.g., linear programming, network flows, discrete optimization, constrained and unconstrained nonlinear programming, queuing theory). Students use computers to explore these topics, but prior computer experience is not assumed. Offered periodically. Prerequisites: MATH 126 or MATH 128, and MATH 220; MATH 226 and/or MATH 262 recommended.
This course investigates the mathematically sophisticated financial models used by large institutional investors to properly price exotic financial instruments and to perform analytic portfolio management. Offered periodically. recommended.
Students work intensively on a special topic in mathematics or its applications. Topics vary from year to year. May be repeated if topic is different. Offered periodically.
Independent work is guided by a faculty member. Students need to have the necessary background, including appropriate coursework, before an independent project is approved. A student may not substitute an IS/IR course for a course regularly offered in a department or program. IS/IR culminates in at least one product (a paper, laboratory report, work of art, etc.). Normally, the student and faculty instructor are expected to meet at least once a week. Prerequisites: at least second-year standing; at least 2 relevant courses for 298 (IS); approval from the faculty instructor, the academic advisor, and the department chair or program director. See catalog for more information under registration and course enrollment.
Credits 1 Total Credits 13 Students must successfully complete the equivalent of 35 or more St. Olaf credits, through a combination of full-credit and fractional-credit courses, one major, and all other degree requirements to earn the Bachelor of Arts degree. *********************************************** For students beginning in Linear Algebra 14 (MATH 220) Course Title Credits
This course continues the study of vector spaces and linear transformations. Topics include: abstract vector spaces; linear transformations, including matrix representations, decompositions such as Jordan Canonical Form and Singular Value Decomposition; characteristic polynomials and the Cayley-Hamilton Theorem; invariant subspaces; and inner product spaces, including orthogonal bases, minimization problems, and the Spectral Theorem. Applications may include graph and network theory, principal component analysis and generalized eigenspaces, iterative solutions of large systems, and representation theory. Offered alternate years. Prerequisites: MATH 220, and MATH 244 or MATH 252.
This course covers partial differential equations from an applied perspective and emphasizes simple models involving phenomena such as wave motion and diffusion. Topics and techniques such as separation of variables, boundary value problems, Fourier series, and orthogonal functions are developed carefully. Mathematical computing is used freely. Offered alternate years. Prerequisite: MATH 226 and MATH 230.
This course covers fundamental concepts of graph theory and their applications, including topics such as simple graphs and directed graphs, degree sequences, Eulerian and Hamiltonian graphs, trees and spanning trees, matchings, networks and feasible flows, connectivity, and graph colorings. Other applications and algorithms may include greedy algorithms for minimum spanning trees, Prüfer codes, Hall's Theorem, the Gale-Shapley Algorithm, Menger's Theorem, the Max-Cut/Min-Flow Theorem, the Committee Scheduling Problem, Kuratowski's Theorem, and Ramsey's Theorem. Offered alternate years. Prerequisites: MATH 244 or MATH 252.
Complex analysis treats the calculus of complex-valued functions of a complex variable. Familiar words and ideas from ordinary calculus (limit, derivative, integral, maximum and minimum, infinite series) reappear in the complex setting. Topics include complex mappings, derivatives, and integrals; applications focus especially on the physical sciences. Offered annually. Prerequisite: MATH 220, and MATH 226 or MATH 244.
The main topics of this course are measure theory on the real line, the Lebesgue integral and its relation to the Riemann integral, and convergence theorems for the Lebesgue integral. Applications to probability and harmonic analysis may be included. Offered alternate years. Prerequisite: MATH 244.
This course is an introduction to topological spaces and their structures mainly from the point-set perspective. Standard topics include separation axioms, compactness, and connectedness. Other topics from geometric and algebraic viewpoints may be included. Offered alternate years. Prerequisite: MATH 244.
This course is a continuation of the study of the theory of groups, rings, and fields. Topics include group actions, Sylow theory, and Galois theory. Other topics may include representation theory, module theory, and others. Offered alternate years. Prerequisite: MATH 252.
Properties of axiomatic systems are illustrated with finite geometries and applied in a synthetic examination of Euclid's original postulates, well-known Euclidean theorems, and non-Euclidean geometries. Euclidean, similarity, and affine transformations are studied analytically. These transformations are generalized to obtain results in hyperbolic geometry and used to generate fractals in an exploration of fractal geometry. Dynamic geometry software and hands-on labs are used to explore both the transformations and properties of these geometries. Offered annually during January Term. Prerequisite: MATH 220, and MATH 244 or MATH 252.
This course covers basic enumeration, including generating functions, recursion, and the inclusion-exclusion principle. Basic combinatorial objects such as set partitions, permutations, integer partitions, and posets are discussed. Making conjectures and proving theorems combinatorially are emphasized. Students also explore topics in graph theory, matrix theory, and representation theory. Offered alternate years. Prerequisite: MATH 244 or MATH 252.
Students work intensively on a special topic in applied mathematics. Topics vary from year to year. May be repeated if topic is different. Offered periodically.
This course provides a comprehensive research opportunity, including an introduction to relevant background material, technical instruction, identification of a meaningful project, and data collection. The topic is determined by the faculty member in charge of the course and may relate to their research interests. Offered periodically. May be offered as a 1.00 credit course or .50 credit course. Prerequisite: determined by individual instructor. OLE Core Requirement: OLE Experience in Practice.
Independent work is guided by a faculty member. Students need to have the necessary background, including appropriate coursework, before an independent project is approved. A student may not substitute an IS/IR course for a course regularly offered in a department or program. IS/IR culminates in at least one product (a paper, laboratory report, work of art, etc.). Normally, the student and faculty instructor are expected to meet at least once a week. See catalog for more information under registration and course enrollment. Prerequisites: at least second-year standing; at least 5 relevant courses for 398 (IR); approval from the faculty instructor, the academic advisor, and the department chair or program director.
