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Mathematics

Requirements & Courses

  • Major Requirements
    1. Thirty-six credits in Mathematics, which must include:
      • MTH-121, 122, 210, 223, 310, and 421 or 431.
      • Twelve other upper-level credits, at least four of which must be at the 300- or 400-level.
    2. Cognates:
      • A computer science course numbered CSC-121 or higher. For students with no previous computer science experience, this will require a prerequisite course of CSC-119 or
      • One non-MTH course, approved by the Department, with a Mathematics prerequisite numbered MTH-113 or higher.
    3. Successful completion of the Major Field Test in Mathematics.
  • Minor Requirements

    Twenty-four credits in Mathematics, which must include:

    1. MTH-121, 122, 210
    2. At least eight other upper-level credits in MTH.
  • Secondary Teaching Major Requirements
    • MTH-120, 121, 122, 210, 223, 242, 310, 411, 421.
    • Cognates:
      • Any 4-credit CSC course. The recommended course is CSC-118.
      • One non-MTH course with a Mathematics prerequisite numbered MTH-113 or higher.
    • Successful completion of the Major Field Test in Mathematics.
  • Secondary Teaching Minor Requirements

    At least twenty-six credits which must include: MTH-120, 121, 122, 223, 411; 117 or 310; and 116 or 341.

  • Mathematics Teaching Major Requirements (PK-6)

    Thirty-six credits which must include:

    1. MTH-110, 117, 121, 122, 202 or 204, 203, 210, 223, 341
    2. Four other upper-level credits in Mathematics
    3. Cognate: CSC-118 or 120
    4. The senior comprehensive, which includes 1) submission of an approved writing sample, and 2) an approved oral presentation.
  • PK-6 Teaching Minor Requirements

    Twenty-four credits which must include:

    1. MTH-110; 113 or 121; MTH-116 or 341; MTH-120 or 223; 204
    2. Four additional credits at MTH-110 or above, excluding 203, 205, and 206
  • Mathematical Sciences Major Requirements

    Fifty-two credits which must include:

    1. MTH-121, 122, 210, 223, 310, 336, 341, and 421 or 431
    2. Computer Science 120 and 121
    3. Twelve additional credits in upper-level Mathematics or Computer Science courses, at least four credits of which must be Computer Science. Courses which combine applications and theory are encouraged (e.g. MTH-211, 342, 391, 399 or 499; and CSC-240, 310, 420, 430, 440, or 499).
    4. The senior comprehensive examination includes three parts: successful completion of the Major Field Test in Mathematics, submission of an approved writing sample and an approved oral presentation.
  • Requirements for Honors in Mathematics
    1. A strong program of mathematics courses: at least five courses at the 300- or 400-level, including both MTH-421 (Abstract Algebra) and MTH-431 (Advanced Calculus).
    2. A grade point average of at least 3.5 in Mathematics major courses
    3. A project including both a paper and oral presentation of honors quality
  • Program Considerations
    • MTH-100, 202, 203, 204, 205, and 206 do not count toward the Mathematics minor.
    • At least one statistics course is recommended.
    • Students interested in graduate school in mathematics should complete both MTH-421 and 431 and an honors project. Students interested in business and industrial careers should consider additional courses in Applied Mathematics, Computer Science and fields which apply mathematics in significant ways.
  • Restrictions

    The following combinations of double majors are not permitted: Mathematical Sciences and Mathematics; and Mathematical Sciences and Computer Science.

Courses

  • MTH
    100
    .
    Applied Algebra
    4 credits
    Develops mathematical skills with an emphasis on increasing the students’ ability to interpret and reason with quantitative information. Focuses on mathematical critical thinking and problem solving. Topics include variables and functions, linear, quadratic, exponential and other models, each presented in the context of applications from social and natural sciences, business, and everyday life.
  • MTH
    108
    .
    Introduction to College Math
    2 credits
    Strengthen your mathematical skills in preparation for coursework requiring quantitative reasoning. Topics include algebraic and exponential expressions, polynomial and rational equations, and graphs in the coordinate system. Emphasis will be placed on the development of critical thinking and problem solving skills through applications.
  • MTH
    110
    .
    Liberal Arts Mathematics
    4 credits
    Prerequisite: MTH-100 or Placement
    Exploration of the beauty, extent and power of mathematics. Specific topics to be selected by the instructor.
  • MTH
    111
    .
    College Algebra With Applications
    4 Credits
    Establishes problem-solving and critical thinking skills through applications. Topics include number systems, algebraic expressions and equations, and a variety of functions including linear, quadratic, exponential, and logarithmic. Intended for students who will take MTH-112 or will encounter quantitative reasoning in multiple courses.
  • MTH
    112
    .
    Pre-Calculus
    4 credits
    Prerequisite: MTH-100 or Placement
    Foundational concepts for the study of calculus. Investigates polynomial, rational, exponential, logarithmic and trigonometric functions. Explores the ideas of functions and graphs, with emphasis on concepts and skills central to calculus. May not be taken for credit by students who have successfully completed MTH-121, 122 or 210.
  • MTH
    113
    .
    Applied Calculus
    4 credits
    Prerequisite: MTH-112 or Pre-Calculus in High School
    Introduction to differential and integral calculus. Focuses on applications; theory held to a minimum. Examples from business and the natural and social sciences. Background in trigonometry not needed.
  • MTH
    116
    .
    Elementary Statistics
    4 credits
    Prerequisite: MTH-100 or Placement
    Introduction to modern elementary statistics and applications. Focuses on statistical reasoning and data analysis. Includes statistical design of experiments, estimation, hypothesis testing, regression, correlation and other selected topics.
  • MTH
    117
    .
    Intro to Matrices and Linear Methods
    2 credits
    Prerequisite: MTH-112 or Pre-Calculus in High School
    Introduction to solving systems of linear equations, linear programming, elementary matrix theory, and the modeling of situations which are linear. Applications from business and natural and social sciences. Note: The content of this course is necessary background for MTH-310. Requires placement in MTH-112 or 4 years of high school math.
  • MTH
    118
    .
    Biostatistics
    4 credits
    Prerequisite: MTH-100 or Placement
    Introduction to statistical methods used in biomedical science and public health research. Focuses on experimental design, descriptive methods, hypothesis tests, analysis of variance, regression, and other selected topics.
  • MTH
    120
    .
    Discrete Mathematics
    4 credits
    Prerequisite: MTH-112 or Pre-Calculus in High School
    Introduction to formal logic, sets, functions and relations, counting methods, graphs and trees, and recursive structures and inductive reasoning.
  • MTH
    121
    .
    Calculus I
    4 credits
    Prerequisite: MTH-112 or Pre-Calculus in High School
    Introduction to the calculus of one variable. Includes limits and continuity, the derivative and applications, the integral and applications, infinite series and sequences. (Part I of II)
  • MTH
    122
    .
    Calculus II
    4 credits
    Prerequisite: MTH-121
    Introduction to the calculus of one variable. Includes limits and continuity, the derivative and applications, the integral and applications, infinite series and sequences. (Part II of II)
  • MTH
    180
    .
    Topics in Mathematics
    2-4 credits
    Selected topics of current or historic importance. Prerequisites vary with topics selected.
  • MTH
    192
    .
    Mathematical Modeling
    4 credits
    Prerequisite: MTH-113 or MTH-121
    Development of various mathematical models used in business, social sciences and biological sciences; uses and limitations of models in practical situations. Some models use calculus and/or the computer. Computer programming not a prerequisite.
  • MTH
    203
    .
    Math - Middle and HS Teachers
    2 credits
    Prerequisite: MTH-121
    This course will provide an overview and examination of the mathematical topics and pedagogical approaches in the middle and high school curriculum. Topics include problem solving, number theory, algebraic thinking, geometry, probability and statistics, and mathematics software applications for teaching (e.g., Geometer’s Sketchpad and TinkerPlots).
  • MTH
    204
    .
    Number Systems for PK-6 Teachers
    4 credits
    Introduction to number systems and operations, including early algebraic thinking, problem solving, set theory, and elementary logic. Analysis and construction of effective mathematical tasks in teaching number systems and operations at the PK-6 level.
  • MTH
    205
    .
    Rational Numbers for PK-6 Teachers
    4 credits
    Unpacking mathematical content and identifying competence for rational numbers, with a focus on representations, learning trajectories, performing and supporting mathematical explanations, and interpreting and extending mathematical thinking.
  • MTH
    206
    .
    Geometry for PK-6 Teachers
    4 credits
    An exploration of 2-D and 3-D geometry topics and spatial relations while exploring the high leverage teaching practice of assessment, noticing student thinking, and using representations.
  • MTH
    210
    .
    Multivariable Calculus
    4 credits
    Prerequisite: MTH-122
    Continuation of Math 122. Includes functions of several variables, vectors, vector-valued functions, three-dimensional analytic geometry, partial differentiation and multiple integration.
  • MTH
    211
    .
    Differential Equations
    4 credits
    Prerequisite: MTH-210
    Techniques and theory of solving ordinary differential equations. Includes series solutions, numerical methods and applications.
  • MTH
    221
    .
    Introduction to Cryptography
    4 credits
    Prerequisite: MTH-122
    Introduction to the mathematics from several different branches of the subject including number theory, matrix algebra, probability, and statistics, all of which play a role in enciphering and deciphering secret messages.
  • MTH
    223
    .
    Mathematical Structures
    4 credits
    Prerequisite: MTH-120 or MTH-122
    Introduction to proof techniques. Theoretical analysis of discrete structures such as sets, graphs, functions, and relations.
  • MTH
    241
    .
    Financial Mathematics
    4 credits
    Prerequisite: MTH-122
    Introduction of fundamental concepts of interest theory. Applications of those concepts in calculating present and accumulated values for various streams of cash flows. Topics include reserving valuations, pricing, asset/liability management, investment income, and capital budgeting. Financial instruments such as derivatives will also be introduced.
  • MTH
    242
    .
    Applied Statistical Methods
    4 credits
    Prerequisite: A MTH course numbered 112 or above, or DAT-115 or 116, or ECN-217, or PSY-220
    Applied study of inferential and descriptive statistics. Topics include data visualization, confidence intervals and hypothesis tests, linear regression, ANOVA, ANCOVA, categorical data analysis, resampling methods, and time series. Emphasizes written and oral communication of results. Uses statistical software, such as R.
  • MTH
    280
    .
    Topics in Mathematics
    2-4 credits
    Prerequisite: MTH-122 or Permission.
    Selected topics of current or historic importance. Prerequisites vary with topics selected.
  • MTH
    280M
    .
    Topics in Mathematics
    2-4 credits
    Selected topics of current or historic importance. Prerequisites vary with topics selected.
  • MTH
    310
    .
    Linear Algebra
    4 credits
    Prerequisite: MTH-210; MTH-117 Strongly Recommended
    Study of finite-dimensional real vector spaces; kernel, dimension, basis, linear transformations and their matrices, and eigenvalues.
  • MTH
    323
    .
    Complex Analysis
    4 credits
    Prerequisite: MTH-210
    Introduction to the theory of functions of a single complex variable. Analytic functions, complex series, Cauchy’s theorem and conformal mapping.
  • MTH
    336
    .
    Numerical Analysis
    4 credits
    Prerequisite: MTH-122 and CSC-120
    Analysis and implementation of numerical algorithms for approximating functions, derivatives and integrals, and for solving nonlinear equations, ordinary differential equations and systems of linear equations. Discussion of standard software packages and techniques for writing efficient and reliable mathematical software in Pascal and/or FORTRAN.
  • MTH
    341
    .
    Probability and Statistics I
    4 credits
    Prerequisite: MTH-122
    In-depth examination of probability and introduction to mathematical statistics. Topics include axiomatic probability, discrete and continuous random variables, transformations of random variables, moment generating functions, limit theorems, and point estimation.
  • MTH
    342
    .
    Probability and Statistics II
    4 credits
    Prerequisite: MTH-341
    Continuation of MTH-341, focusing on mathematical statistics. Selected topics may include maximum likelihood estimation, likelihood ratio tests, linear models, and Bayesian methods.
  • MTH
    345
    .
    Stochastic Processes
    4 credits
    Prerequisite: MTH-210
    Introduction to the theory and applications of stochastic processes, including Markov chains, Poisson processes, queuing theory, and Brownian motion. Example applications include models of random walks, DNA sequences, call centers, and the Black-Scholes option pricing formula.
  • MTH
    351
    .
    Elementary Number Theory
    4 credits
    Prerequisite: MTH-223
    Study of integers, including divisibility, the theory of prime numbers, congruences and solutions of equations in integers.
  • MTH
    380
    .
    Topics in Mathematics
    4 credits
    Selected topics of current or historic importance. Prerequisites vary with topics selected.
  • MTH
    390
    .
    Combinatorics
    4 credits
    Prerequisite: MTH-120 or 122
    Introduction to combinational theory. Topics include enumeration, recurrence, generating functions, graph theory and optimization.
  • MTH
    390M
    .
    Combinatorics
    4 credits
    Prerequisite: MTH-120 or 122
    Introduction to combinational theory. Topics include enumeration, recurrence, generating functions, graph theory and optimization.
  • MTH
    391M
    .
    Introduction to Graph Theory
    4 credits
    Prerequisite: MTH-122 or Permission
    Introductory survey of the major concepts and applications of graphs, digraphs and networks. Application areas include transportation, traffic flow, games and puzzles. Spring Term only.
  • MTH
    411
    .
    College Geometry
    4 credits
    Prerequisite: MTH-223
    Axiomatic systems, models, finite geometries, Hilbert’s axioms, independence of the parallel postulate, and introduction to non-Euclidean geometries with emphasis on hyperbolic geometry.
  • MTH
    413
    .
    Topology
    4 credits
    Prerequisite: MTH-223
    Introduction to point-set topology. Includes topological properties of Euclidean spaces, abstract spaces and metric spaces. Explores connectedness, compactness, continuity and homeomorphisms.
  • MTH
    421
    .
    Abstract Algebra
    4 credits
    Prerequisite: MTH-223 and 310
    Introduction to the theory of algebraic structures including elementary theory of groups, rings and fields.
  • MTH
    431
    .
    Advanced Calculus
    4 credits
    Prerequisite: MTH-210 and 223
    In-depth examination of the calculus of one variable, including topology of the real line, sequences and series of functions.
  • MTH
    491
    .
    Mathematical Methods of Physics
    4 credits
    Prerequisite: MTH-211; MTH-310 recommended
    Survey of advanced mathematical topics for application in the physical sciences. Topics selected from Fourier series, transform calculus, partial differential equations, boundary value problems, complex variables and vector calculus. Highly recommended for students planning graduate study in the physical sciences or applied mathematics.
  • MTH
    499
    .
    Mathematics Independent Study
    1 credit
    Requires instructor permission.
  • MTH
    500
    .
    Senior Thesis
    4 credits
    Requires instructor permission.