Associate Professors: Anita Goldner, Mohammad Salmassi

All students must complete the following twelve (12) core courses:

In addition to the twelve (12) core requirements above, each student must complete:

43.222 Differential Equations

43.427 Real Analysis

Six (6) electives from mathematics, physics, computer science, or an approved minor

In addition to the twelve (12) core requirements above, each student must complete:

43.222 Differential Equations

43.427 Real Analysis

42.200 Psychology of Development

14.200 Education in American Society with Field Study I

14.315/ Professional Preparation and Field 14.316 Study II: Methods, Special Education and Technology: High School/Middle School (Credit - two courses)

14.410 Student Teaching Practicum and Seminar I- Secondary (Credit-two courses)

14.411 Student Teaching Practicum and Seminar II - Secondary (Credit-two courses)

Note: Mathematics Department prerequisites for 14.315 Professional Preparation and Field Study II - High School and 14.316 Professional Preparation and Field Study II - Middle School are completion of:

All required mathematics courses except:

43.319 Abstract Algebra

43.427 Real Analysis

Prerequisites for 14.410-411 Student Teaching Seminar and Practicum I-II - High School and 14.414-15 Student Teaching Seminar and Practicum I-II - Middle School are completion of all department requirements, plus 14.315 Professional Preparation and Field Study II - High School or 14.316 Professional Preparation and Field Study II - Middle School, depending on the level.

In addition to the twelve (12) core requirements listed above, each student must complete:

43.110 College Mathematics I

It is strongly recommended that students select 43.201 Intuitive Geometry and 43.301 Problem Solving and Modeling in Mathematics as the two mathematics electives among the core courses.

B. Coordinate Major in Elementary Education (Grades 1 - 6 Licensure)

43.219 Calculus I and four (4) courses at or above the 200-level. Students may substitute 43.117 Introduction to Statistics for 43.200 Precalculus but only one of these courses may receive credit towards the mathematics minor. These courses are to be chosen under the guidance of a member of the Mathematics Department.

Plus two (2) electives from:

A non-credit course covering the essentials of high school algebra. Time will be spent on common arithmetic difficulties and elementary metric geometry.

Prerequisite: Permission of the Mathematics Department.

43.110 College Mathematics I (Gen.Ed. Goal 2)

An exploration of numbers, their representations, relationships, and uses; arithmetic; elementary set theory; basic logic; geometry; measurement; probability; and statistics. This course offers a college-level treatment of content areas of interest to prospective early childhood and elementary teachers. Problem-solving and the communication of mathematical ideas, both verbally and algebraically, are woven throughout the course. Note: Students may not receive credit for both 43.110 and 43.113 Introduction to College Mathematics.

Prerequisite: Satisfactory score on the mathematics placement examination or permission of the Mathematics Department.

An introduction to the discipline of statistics, emphasizing both statistical thinking and its application to analyzing data. Topics include sampling, design of experiments, organizing and exploring data, probability distributions such as the normal distribution, sampling distributions, hypothesis testing and confidence intervals, correlation and regression. Students are expected to express results of statistical procedures in ordinary non-technical language. Real world applications of statistical topics are emphasized throughout the course.

Prerequisite: Satisfactory score on the mathematics placement examination or permission of the Mathematics Department.

A survey of the beauty and effectiveness of mathematics in describing natural and social phenomena. Topics may include pattern recognition, logic, sets, number systems, counting methods, probability, statistics, symmetry, population growth, voting systems, or consumer mathematics. This course is recommended for students whose major does not require 43.110 College Mathematics I, or 43.117 Introduction to Statistics, or 43.123 College Algebra.

Prerequisite: Satisfactory score (1 or higher) on the mathematics placement exam.

A continuation of 43.110 College Mathematics I, providing further exploration of numbers and arithmetic, geometry, measurement, probability, and statistics from the point of view of prospective early childhood and elementary school teachers. As in 43.110, problem solving and the communication of mathematical ideas, both verbally and algebraically, are strands that unite the course.

Prerequisite: 43.110 College Mathematics I.

43.123 College Algebra (Gen.Ed. Goal 2)

Designed to provide the algebraic skills needed in the natural sciences, social sciences, and precalculus. The course emphasizes problem-solving skills, modeling and real-world applications, and explores multiple approaches (numerical, graphical, and symbolic) to algebraic concepts and problems. Topics include the real number system, algebraic expressions, functions and graphs, polynomial and exponential functions, matrices and systems of equations, and complex numbers. Note: A student may not receive credit for both 43.123 and 43.115 College Algebra and Trigonometry.

Prerequisite: 43.095 General Mathematics or a satisfactory score on the mathematics placement examination.

A thorough introduction to the basic mathematical functions used in the sciences and the background needed to study calculus. After a brief in-depth review of the required algebra and analytical geometry, topics include functions and graphs, polynomial and rational functions, exponential and logarithmic functions, and trigonometric functions. Note: A student may not receive credit for 43.200 Precalculus and 43.133 Precalculus, or for 43.200 Precalculus and 43.115 College Algebra and Trigonometry.

Prerequisite: 43.123 College Algebra or a satisfactory score on the mathematics placement examination.

An introduction to the fundamental ideas of geometry for prospective teachers. Geometric objects and relationships are studied through intuitive, coordinate, vector and synthetic approaches. The course builds from an informal approach, stressing visualization in two and three dimensions, to the development of mathematical reasoning.

Prerequisite: One credit-bearing course in college mathematics or permission of the instructor.

43.208 Biostatistics

A course that covers statistical methods as they apply to the biological, health, and food sciences. The major emphasis is on hypothesis testing, including regression and analysis of variance. Descriptive statistics is also included. The statistical package Minitab is used. Note: A student may not receive credit for both 43.208 Biostatistics and 43.117 Introduction to Statistics or 23.304 Biometrics.

Prerequisite: One credit-bearing course in college mathematics.

A study of mathematical models in various disciplines. Topics include logic, sets, functions, combinatorics, probability, matrices, Markov chains, linear programming, game theory, and digraphs.

Prerequisite: 43.200 Precalculus or permission of the instructor.

A study of functions, limits, continuity, the derivative, rules of differentiation of algebraic and trigonometric functions, applications of differentiation, definite and indefinite integrals, the Fundamental Theorem of Calculus, and applications of integration.

Prerequisite: 43.200 Precalculus or a satisfactory score on the mathematics placement examination.

A study of the applications of the integration, logarithmic and exponential functions, elementary differential equations (first order linear and separable variables), techniques of integration, improper integrals, L'Hospital's Rule, sequences, series, Taylor and Maclaurin Series, application of series.

Prerequisite: 43.219 Calculus I.

A study of conic sections; vectors in two and three dimensions; dot and cross products and their applications to geometry; equations of lines and planes; quadratic surfaces; polar, cylindrical, and spherical coordinates; and functions of several variables, partial derivatives, differentials, directional derivatives, gradients, optimization problems, multiple integrals and their applications.

Prerequisite: 43.220 Calculus II.

A study of the methods for solving linear and elementary nonlinear differential equations with special emphasis on applications in the sciences. Topics covered include equations of the variable separable type; exact, homogeneous and Bernoulli equations; the method of substitution; approximation methods; linear equations; series techniques; Laplace transforms; systems of equations; and the Sturm-Liouville theory.

Prerequisites: 43.220 Calculus II and 43.226 Linear Algebra and Applications.

A study of vector spaces, subspaces, linear dependence, bases, dimension, linear mappings, linear equations, matrices, inner products and norms, determinants, quadratic forms, and the spectral theorem. Applications to various fields outside of mathematics are examined.

Prerequisites: 43.215 Finite Mathematics and 43.220 Calculus II.

A mathematical foundation for computer science. Topics include logic, boolean algebra, sets, functions, sequences, and summations, matrices, mathematical induction, study of algorithms, recursion, combinatorics, graphs, and trees. Note: A student may not receive credit for both 43.292 Discrete Mathematics I and 43.320 Discrete Mathematics.

Prerequisites: 43.200 Precalculus and 63.252 Computer Science II, or permission of the instructor.

A study of discrete mathematical structures. Topics include a brief review of sets and an exploration of relations, graphs, trees, digraphs, finite-state machines, formal languages, boolean algebra, and combinatorial circuits.

Prerequisite: 43.292 Discrete Mathematics I.

A study in problem solving with the development of banks of problems appropriate to various grade levels and selected from arithmetic, informal geometry, logic, measurement, number sequences, probability, and statistics, challenging enough to provoke interest, but realistic enough for successful experiences. Heuristics, problem solving techniques, Polya’s stages of problem solving, specific strategies, and pedagogical issues are studied.

Prerequisite: 43.201 Intuitive Geometry and 43.215 Finite Mathematics.

A study of regression and correlation analysis, chi square tests and contingency tables, design of experiments, analysis of variance, non-parametric statistics, and introduction to data analysis.

Prerequisite: 43.117 Introduction to Statistics or 43.208 Biostatistics.

Practical aspects of data analysis using statistical computer packages such as MINITAB, SPSSX, AND BMDP. Multivariate statistical methods including multiple regression, analysis of covariance, factor analysis, multidimensional scaling, discriminant analysis and linear models for cross-classified categorical data are emphasized. Students do individual data analysis projects.

Prerequisite: 43.307 Intermediate Statistics.

A study of properties of numbers. Topics include mathematical induction, divisibility, primes, congruences, the Chinese remainder theorem, primitive roots, quadratic reciprocity, continued fractions, partitions, and history of classical problems.

Prerequisite: 43.220 Calculus II.

A study of topics from elementary numerical analysis: finite differences, solution of equations, interpolation, numerical integration, and numerical linear algebra. Computer exercises and applications. This course is recommended as preparation for the numerical analysis half of the Part 3 Actuarial Exam.

A precise, rigorous examination of the axioms and concepts of various geometries. Euclidean, non-Euclidian, and transformational geometries are investigated. Ruler-compass constructions are discussed.

Prerequisites: 43.219 Calculus I

A study of algebraic structures and related concepts including sets, logic, mappings, the integers, the division algorithm, groups, rings, integral domains, fields, and polynomials. Note: A student may not receive credit for both 43.319 Abstract Algebra and 43.335 Algebraic Structures I.

Prerequisite: 43.310 Number Theory.

Vector differential calculus, vector integral calculus including the theorems of Green, Gauss and Stokes, maxima and minima for functions of several variables, Language multipliers, uniform covergence of sequences and series of functions, inverse and implicit function theorems, and Jacobians.

Prerequisite: 43.221 Calculus III, 43.226 Linear Algebra and Applications.

The study of problems arising from real-world situations and the mathematical methods used in their solution. Topics include mathematical modeling, continuous and discrete models, linear systems, Fourier series, partial differential equations, and computer implementation of solutions.

Prerequisite: 43.222 Differential Equations, 63.152 Computer Science I Using C, and a course in probability, statistics or finite mathematics; or permission of the instructor.

Sample spaces, events as subsets of a sample space, probability axioms, combinatorics applied to probability problems, random variables and their distributions, special distributions, multivariate distributions, central limit theorem, and topics in statistical inference.

Prerequisite: 43.221 Calculus III plus either 43.215 Finite Mathematics or 43.226 Linear Algebra and Applications.

Estimation, decision theory and hypotheses testing, linear models, regression, analysis of variance, analysis of categorical data, and nonparametric inference.

Prerequisite: 43.348 Mathematical Statistics I.

An exploration of an advanced topic in mathematics or computer science. The particular topic is announced at least one semester in advance.

Prerequisite: Permission of the instructor.

Set theory, relations and functions, properties of the real number system, topology of the real line, introduction to metric spaces, limits of sequences and functions, continuous functions, differentiation, and the Riemann-Stieltjes integral.

Prerequisite: 43.221 Calculus III.

Student research on a topic or topics in higher mathematics or computer science. Suggested areas include applied algebra, numerical analysis, and mathematical physics. The student should make arrangements with the faculty member who is to direct the work one semester in advance of the work.

The student is encouraged (and assisted to whatever extent possible) by the Mathematics Department to seek employment during summers or part time during the school year, involving non-trivial applications of mathematics. In this manner the student can earn up to three (3) course credits, the amount of credit being decided by the student’s advisor and the department chair.

Prerequisite: Approval of the chair.