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Mathematics & Statistics Courses
Below 100-Level Courses
MAT 095/Intermediate Algebra
additive credit
(every semester)
Prerequisites: Satisfactory completion of the academic development required in mathematics; demonstrated inadequate level of preparation for MAT 096
This course is designed for students majoring in a field where at least one of the courses, Calculus A (MAT 127) or Calculus for Business and the Social Sciences (MAT 125) is required. Conceptual understanding and skill development of traditional algebraic topics such as: linear equations and inequalities, exponents and polynomials, rational expressions, quadratic equations, and systems of linear equations are included.
MAT 096/Pre-Calculus
additive credit
Formerly MATH 120
(every semester)
Prerequisite: MAT 095 or placement into MAT 096
This course is only for students going on to calculus. Fundamentals of algebra, trigonometry, and analytic geometry. Stress is on computational and problem-solving techniques.
MAT 099/Orientation to Mathematics & Statistics
0 course unit
(seven weeks)
(every semester)
Required as an entry course of all entering freshmen and transfer students enrolled in majors offered by the Department of Mathematics and Statistics. Topics covered include degree requirements, general information about the College and services offered, career opportunities in mathematics and statistics, academic standards and integrity, study habits and time management, and resume development. General and personal advisement relative to pursuit of the major and the degree is also included.
100-Level Courses
MAT 101/Applied Liberal Arts Mathematics
1 course unit
(every semester)
Provides intuitive and formal experience in development and appreciation of structural bases characteristic of mathematics. Topics from: graph theory, coding, voting, and social choice and game theory.
MAT 102/Mathematics for the Liberal Arts
1 course unit
(every semester)
Provides intuitive and formal experience in development and appreciation of structural bases characteristic of mathematics. Topics from: combinatorial probability, abstract mathematical systems, and number theory.
MAT 105/Mathematical Structures and Algorithms for Educators I
1 course unit
(every semester)
This course concerns the development of number systems, algebraic structures, and algorithms. The student will be required to reason mathematically, solve problems, and communicate mathematics effectively at different levels of formality, using a variety of representations of mathematical concepts and procedures. Physical materials and models will be used to explore fundamental properties of number systems, to model algorithms, and to explore selected algebraic structures. This course is especially appropriate for those students preparing to be elementary, early childhood, or special education teachers.
MAT 106/Mathematical Structures and Algorithms for Educators II
1 course unit
(every spring)
Physical materials and models will be used to explore fundamental concepts of geometry, measurement, data analysis, statistics, and probability. The student will be required to reason mathematically, solve problems, and communicate mathematics effectively at different levels of formality, using a variety of representations of mathematical concepts and procedures. This course is especially appropriate for those students preparing to be elementary, early childhood, or special education teachers.
MAT 125/Calculus for Business and the Social Sciences
1 course unit
(every semester)
Prerequisite: MAT 096 or placement into MAT 125 See http://www.tcnj.edu/~mathstat for details
A course intended for majors in business and the social sciences, and/or minors in statistics. Topics include differential calculus, integral calculus, and some linear algebra, with applications to areas of business and social science. Not for mathematics or science majors.
MAT 127/Calculus A
1 course unit
(every semester)
Prerequisite: MAT 096 or placement into MAT 127. See http://www.tcnj.edu/~mathstat for details
Provides students with a solid grounding in single-variable calculus. The course is designed for students in the mathematical and physical sciences. Topics include functions and limits, derivatives and differentiation rules, applications of derivatives, and an introduction to integrals and their applications.
MAT 128/Calculus B
1 course unit
(every semester)
Prerequisite: MAT 125 or 127
A second course in calculus covering integral calculus and series. The course will cover both the theoretical and applied aspects of calculus.
STA 115/Statistics
1 course unit
(every semester)
Introduction to descriptive statistics and statistical inference. Topics include: measures of location and variability, graphical displays, probability, normal distribution, sampling, estimation, and hypothesis testing. A student may not receive credit for both STA 115 and STA 215.
200-Level Courses
MAT 200/Discrete Mathematics
1 course unit
(every semester)
An introduction to discrete mathematics. Discrete topics include sets, graphs, Euler and Hamilton circuits, connectivity, planar graphs, recursion, and difference equations. Descriptions of the proof types such as direct, indirect, cases, contrapositive, and induction included whenever possible. Some optional topics which may be covered are: fractals, algorithms, combinatorial proofs, discrete codes, logic, Platonic solids, and combinatorial counting.
MAT 205/Linear Algebra
1 course unit
(every semester)
Prerequisite: MAT 128 or MAT 200 or CSC 310
An introduction to vector spaces and systems of linear equations essential for the understanding of both pure and applied mathematics. Selected topics include: systems of linear equations, matrices, linear transformations, linear independence, determinants, vector spaces, eigenvalues and eigenvectors, and orthogonality.
MAT 229/Multivariable Calculus
1 course unit
(every semester)
Prerequisite: MAT 128
Topics include: geometry of three dimensional space, derivatives of functions of several variables, integrals in dimension two and three, and Stoke’s theorem.
MAT 255/Perspectives on the Development of Mathematics
1 course unit
(every semester)
The course develops a skeletal outline of the history of mathematics. Additional topics may include the history of a specific area of mathematics. Samples of topics that may be covered in the course are: ancient mathematics, the relation between Greek and Mesopotamian algebra, the growth of trigonometric ideas, the geometric solution of the cubic equations by Omar Khayyam and the algebraic solutions by Cardano, Zeno’s paradox, and the development of different number systems.
MTT 202/Teaching Mathematics in the Early Childhood,
Elementary, and Middle School Classroom
1 course unit
(with field placement)
(every semester)
Prerequisite: MAT 105, MAT 106, or MAT 200 Corequisite: MST 202
This course examines the early childhood, elementary, and middle school mathematics curricula, how children learn mathematics, methods and strategies appropriate for teaching the many topics in mathematics. Students will be introduced to national and state standards for preK–8 mathematics, and learn how to teach according to these standards. Topics include the use of manipulatives and technology in teaching mathematics, learning theories, adaptations for diverse learners, and the investigation of standards-based curricula. A field experience is a critical component of this course. The student will observe and participate in the early childhood, elementary, or middle school classroom of an exemplary mathematics teacher three hours per week.
STA 215/Statistical Inference
1 course unit
(every semester)
Prerequisite: MAT 125 or MAT 127
This course provides a comprehensive introduction to descriptive statistics and the essential ideas of probability. Students will study foundations of classical parametric inference: point estimation, confidence intervals, hypothesis testing, and common statistical techniques including simple regression and correlation. Examples will be drawn from a variety of social and natural sciences.
300-Level Courses
MAT 301/Number Theory
1 course unit
(every semester)
Prerequisite: MAT 200
Divisibility, primes, unique factorization, diophantine equations, congruences, quadratic reciprocity, and such optional topics as sums of squares, number-theoretic functions, continued fractions, prime number theory, public-key encryption, and elliptic curves.
MAT 305/Abstract Algebra
1 course unit
(every semester)
Prerequisites: MAT 200, and MAT 205 or MAT 301
An introduction to groups, rings, integral domains, and fields. Additional topics include groups of symmetries, rings of integers, rings of polynomials, and construction of the field of rational numbers.
MAT 310/Real Analysis
1 course unit
(annually)
Prerequisites: MAT 200 and MAT 229
A logical development of mathematical analysis for functions of a single real variable. Topics include order, completeness, sequences, series, limits of functions, basic topology of the reals, differentiation, integration, sequences and series of functions and transcendental functions.
MAT 315/Topics in Linear Algebra
1 course unit
(periodically)
Prerequisite: MAT 205
The course consists of a collection of topics not covered in MAT 205 but built upon the material covered in MAT 205. Such topics may include: the Spectral Theorem of Symmetric Matrices, Quadratic Forms, Unitary and Hermitian Matrices, Jordan Canonical Forms, Schur’s Theorem, applications to Linear Programming, and Markov chains.
MAT 316/Probability
1 course unit
(every semester)
Prerequisites: MAT 200 and MAT 229
Topics will include counting rules to derive models for discrete variables, including the uniform, Bernoulli, binomial, geometric, negative binomial, hypergeometric, and Poisson distributions. Continuous variables will be modeled with distributions having a variety of shapes, including the uniform, exponential, gamma, beta, and normal distributions.
MAT 320/Complex Analysis
1 course unit
(annually)
Prerequisite: MAT 229
A logical development of the classical theory of functions of a complex variable, with emphasis on those parts of the theory which are most used in modern applications of the subject. Topics include: complex numbers; analytic functions; the exponential, trigonometric, hyperbolic, and logarithmic functions and their inverses; mapping by elementary functions; integrals; the Cauchy-Goursat theorem, the Cauchy integral formula, derivatives of analytic functions; the fundamental theorem of algebra; power series; residues and poles; and isolated, essential, and removable singularities.
MAT 326/Differential Equations
1 course unit
(periodically)
Prerequisite: MAT 229
Presentation of subject through logical and orderly approach with emphasis on general concepts rather than isolated details. Topics: first-order ordinary differential equations, linear differential equations with constant coefficients, simultaneous differential equations, hyperbolic functions, and Laplace Transforms.
MAT 331/Numerical Methods
1 course unit
(periodically)
Prerequisites: MAT 229, MAT 205
Numerical Methods is a course which focuses on methods of approximating solutions to problems for which the techniques of the earlier Calculus courses fail. A course covering methods of approximation, errors in approximation, and efficiency of algorithms.
MAT 351/Geometry
1 course unit
(every semester)
Prerequisites: MAT 200 and MAT 229
In this course both Euclidean and non-Euclidean geometries are studied. Each geometry will be understood from three different perspectives: first, as the collection of theorems following from a particular set of axioms; second, as the two-dimensional geometry arising from a particular metric; and third, as the geometry obtained from a set together with a specific group of rigid motions of the set. At least one of these viewpoints will be developed in detail.
MAT 370/Topics in Mathematics
1 course unit
(occasionally)
MAT 390/Mathematics Specific Research Course
variable course units
MAT 391/Independent Study in Mathematics
variable course units
MAT 392/Guided Study in Mathematics
1 course unit
MAT 393/Independent Research in Mathematics
1 course unit
(every semester)
Prerequisite: By invitation only
Student will study and/or do research independently in an appropriate area. A department member will be assigned to advise and direct the student.
MAT 399/Internship in Mathematics
variable course units
(every semester)
Prerequisites: Junior standing and permission of the department.
Applied experience in major field of study. Consult department for details.
MTT 380/Methods of Teaching Mathematics I
1 course unit
(every fall)
Prequisites: MAT 200, MAT 205, and MAT 229
This course is the first in a two-course sequence of professional courses for mathematics education majors. Students will be introduced to national and state standards for K-12 mathematics,and learn how to teach according to these standards. Topics include the use of manipulatives and technology in teaching mathematics, learning theories, and the investigation of standards-based curricula. These topics will be mostly situated in the content of middle school mathematics.
MTT 390/Methods of Teaching Mathematics II
1 course unit
(every spring)
Prequisites: MTT 380
Corequisites: SED 399 and SPE 323
This course is the second in a two-course sequence of professional courses for mathematics education majors. Students will be familiar with the standards for 9-12 mathematics, and will engage in exploring topics from Discrete Math, Algebra, Geometry, Precalculus, and Calculus. These topics will be examined with the perspective gained from MTT 380 along with that gained from research. Manipulatives, models, software, and calculators will be used to explore appropriate topics from each area. Classroom organization and management will also be explored. The course will be taken as part of a junior block of courses that share a field placement.
STA 303/Design of Experiments
1 course unit
(spring-odd years)
Prerequisites: STA 115 and MAT 125 or MAT 127; or STA 215
This course will introduce students to problems and techniques inherent to the design and analysis of experiments. There are broad applications across numerous disciplines in the sciences and the humanities. Topics include: analysis of variance, blocking, general factorial models, nested designs, confounding, and fractional replication. A statistical software package will be used throughout the course (SAS, SPSS, or MINITAB).
STA 304/Sampling and Nonparametric Statistics
1 course unit
(spring—even years)
Prerequisites: STA 115 and MAT 125 or MAT 127; or STA 215
This course introduces students to the use of sampling theory, the design and analysis of sample surveys, and robust statistical tests that are applicable in a wide range of real-world applications. Topics include: stratified sampling, cluster sampling, quota sampling, questionnaire design, and k-sample tests for paired and unpaired data.
STA 305/Regression Analysis
1 course unit
(every fall)
Prerequisites: STA 115 and MAT 125 or MAT 127; or STA 215
This course presents regression concepts and techniques as a synthesis of theory, methods, and applications. Topics include: multiple regression, interactions, partial and multiple correlation, polynomial regression, and logistic regression. A statistical software package will be used throughout the course (SAS, SPSS, or MINITAB).
STA 306/Applied Multivariate Analysis
1 course unit
(every fall)
Prerequisites: STA 115 and MAT 125 or MAT 127; or STA 215
This course will introduce students to a variety of multivariate statistical methods as aids to analyzing and interpreting large data sets. These methods will have general applications across a wide range of client disciplines. Topics include: principal components analysis, cluster analysis, discriminant analysis, multi-dimensional scaling, and correspondence analysis. A statistical software package will be used throughout the course (SAS, SPSS, or MINITAB).
STA 307/Data Mining and Predictive Modeling
1 course unit
(every spring)
Prerequisites:ECO 231 or PSY 303 or MAT 316 or any 300-level statistics course.
Students will be introduced to a variety of statistical techniques that are widely used in modern data mining.The techniques include decision trees, link functions, logistic regression, neural networks, tree/net, prior vector and profit/loss matrix, two-stage modeling, text mining,missing value imputation techniques, association rules, self-organizing maps, and independent component analysis. Computer technology will be used extensively throughout the course.
STA 314/Statistical Quality Control
1 course unit
(occasionally)
Prerequisites: STA 115 and MAT 125 or MAT 127; or STA 215
An introduction to modern techniques of quality control and reliability practice. Topics include: acceptance sampling, sampling plans, control charts, combinatorial reliability, failure models, and system reliability.
STA 317/Linear Programming
1 course unit
(spring-even years)
Prerequisites: MAT 127 and MAT 205
This course introduces students to the field of operations research, in particular that portion of the field which deals with deterministic problems. Topics include optimization using linear programming techniques, network problems, and applications to problems of transportation and trans-shipment. Operations research software packages are integral to the course.
STA 318/Operations Research
1 course unit
(spring—odd years)
Prerequisite: MAT 316
An introduction to that portion of operations research which deals with probabilistic techniques. Topics include: forecasting, queuing models, inventory control, and simulation. Students will become conversant with a number of operations research software packages.
STA 390/Statistics Specific Research Course
variable course units
STA 391/Independent Study in Statistics
variable course units
STA 392/Guided Study in Statistics
1 course unit
STA 393/Independent Research in Statistics
1 course unit
(every semester)
Prerequisite: By invitation only
Student will study and/or do research independently in an appropriate area. A department member will be assigned to advise and direct the student.
STA 399/Internship I in Statistics
variable course units
(every semester)
Prerequisites: Junior standing and permission of department
A supervised statistics-related experience working for government or the private sector. Based on input from the client, the student and faculty coordinator agree on the overall scope of the project including learning objectives, work plan, and expected outputs. The content of the internship should require the student to do some research and/or creative work. Students will periodically inform the coordinator of status and, on completion of the internship, will document the experience and make an oral presentation. The course counts as a general elective for the student with either a major or a minor in statistics. Grading is Pass/Unsatisfactory. Courses graded on a P/U basis are not counted as part of the 16 course units of letter-graded courses for graduation with honors.
400-Level Courses
MAT 403/Advanced Calculus
1 course unit
(periodically)
Prerequisite: MAT 229
In this course the calculus of several variables is explored from the point of view of the geometry of surfaces in Euclidean space. The emphasis will be on examples rather than proofs. Topics will include the topology of Euclidean Space, the derivative as a linear map, the geometry of maps whose derivative have maximal rank, and Lie groups such as SL (2, R).
MAT 405/Topology
1 course unit
(periodically)
Prerequisite: MAT 305
In this course students will gain acquaintance of various aspects of topology and its connections to analysis and algebra. This will include a thorough treatment of those aspects of point-set topology that lay the foundation for graduate study; i.e., continuity, compactness, connectedness and separation axioms. Also, this course will introduce students to manifold theory, including the classification of two-dimensional manifolds. The student will understand the role of topological invariants in the classifying topological spaces. This will lead to the classification of the surfaces. Lastly, students will see categorical relationships between topological objects and algebraic objects.
MAT 407/Projective Geometry
1 course unit
(occasionally)
Prerequisite: MAT 305
An introduction to projective geometry. Topics include affine and projective plane, real projective plane, principle of duality, groups of automorphisms, and projective planes over division rings.
MAT 440/Mathematical Logic
1 course unit
(occasionally)
Prerequisites: MAT 200 and sophomore standing or above
This course studies the process, characteristics, and limits of logical reasoning. Several logical languages will be developed from first principles. Students will become familiar with theorems on consistency and independence and develop an appreciation of Godel’s incompleteness theorem. An introduction to set theory will be included to discuss infinite cardinals.
MAT 451/Seminar in Algebra
1 course unit
(occasionally)
Prerequisites: MAT 229 and MAT 305
A flexible course in which the content is selected from topics in algebra. This is an elective course designed to enrich the background of the student as well as to bridge the gap between undergraduate math and graduate math.
MAT 452/Seminar in Geometry and Topology
1 course unit
(occasionally)
Prerequisites: MAT 229 and a 300-level MAT course
A flexible course in which the content is selected from topics in geometry and topology. This is an elective course designed to enrich the background of the student as well as to bridge the gap between undergraduate math and graduate math.
MAT 453/Seminar in Analysis
1 course unit
(occasionally)
Prerequisites: MAT 229 and MAT 310
A flexible course in which the content is selected from topics in analysis. This is an elective course designed to enrich the background of the student as well as to bridge the gap between undergraduate math and graduate math.
MAT 454/Seminar in Applied Mathematics
1 course unit
(occasionally)
Prerequisites: MAT 229 and a 300-level MAT course
A flexible course in which the content is selected from topics in applied mathematics. This is an elective course designed to enrich the background of the student as well as to bridge the gap between undergraduate math and graduate math.
MAT 470/Topics in Mathematics
1 course unit
(occasionally)
MAT 493/Independent Research II in Mathematics
1 course unit
(every semester)
Prerequisite: By invitation only
Student will study and or do research independently in an appropriate area. A department member will be assigned to advise and direct the student.
MAT 494/Independent Study in Mathematics
variable course units
(every semester)
MAT 498/Capstone
0 course unit
(every semester)
Prerequisite: Senior standing
Intensive study of advanced topics in mathematics. Students will write and present an expository paper.
MTT 490/Student Teaching
2 course units
(every semester)
Prerequisites: MTT 390 and meeting all the criteria for admission for student teaching including completion of all required mathematics courses and cummulative average of at least 2.75.
Corequisite: SED 498
Student Teaching during the senior year under direct supervision of approved public school and general supervision of college supervisors. Observation, participation, and responsible teaching.
MTT 491/Global Student Teaching
2 course units
(every semester)
Prerequisites: MTT 390 and meeting all the criteria for admission for student teaching including completion of all required mathematics courses and cumulative average of at least 2.75.
Corequisite: SED 498
Student teaching abroad during the senior year under direct supervision of approved public school and general supervision of college supervisors. Observation, participation, and responsible teaching. Student will spend half of the semester abroad and half in a local school.
STA 410/Mathematical Statistics
1 course unit
(every fall)
Prerequisites: STA 215 and MAT 316
Topics include: theory of sampling, law of large numbers, central limit theorem, normal approximation to binomial and poisson distributions, estimation of population parameters, hypothesis testing, confidence methods, change of variable, and order statistics.
STA 492/Internship II in Statistics
variable course units
(every semester)
Prerequisites: Junior standing and permission of department
A supervised statistics-related experience working for the government or the private sector, in which the student will be expected to include research as part of the project. Based on a general description of the project from the client, the student, working with the TCNJ faculty coordinator, will structure the project. The structure will include the learning objectives, the research issues, the projected work plan, and the possible results. Students will periodically inform the faculty coordinator of status and progress. On completion, the student will formally document the project for the client and TCNJ. The student will also make an oral presentation that is open to the public. The course can count as an option in the statistics major or minor or as a general elective. A letter grade will be assigned by the faculty coordinator based on input from the client, as well as from the written and oral presentation.
STA 494/Seminar in Statistics
1 course unit
(occasionally)
Prerequisite: Permission of department
An investigation of selected areas of the field through the use of journal articles and monographs, and the solution of problems which may be outside the scope of other course requirements.
STA 498/Capstone
1 course unit
(every semester)
Prerequisite: Senior standing
Intensive study of advanced topics in statistics. Students will write and present an expository paper on their topic of choice.
