**Course Descriptions and Syllabi**

- Below 100-Level Courses
- 100-Level Courses
- 200-Level Courses
- 300-Level Courses
- 400-Level Courses
- 500-Level Courses

### Writing Resources

## Below 100-Level Courses

*Courses marked as additive credit are considered credit-bearing for the purposes of financial aid, tuition, and the determination of full-time student status, but do not count towards graduation credits.*

**MAT 095/Intermediate Algebra
0.5 units (additive credit – does not count towards graduation)**

(every semester)

*See https://mathstat.tcnj.edu/courses-2/calculus-requirement/ for details. This course is designed for students majoring in a field where at least one of the courses, Pre-Calculus (MAT 096), 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. Click here for syllabus (PDF).*

Prerequisites:

Prerequisites:

**MAT 099/Orientation to Mathematics and Statistics
0 course units**

(seven weeks long, every semester)

Required as an entry course of all entering first-year 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. Click here for syllabus (PDF).

## 100-Level Courses

**MAT 101/Applied Liberal Arts Mathematics
1 course unit**

(every semester)

A liberal arts course covering applied topics in modern mathematics. Topics from: graph theory, coding, voting, and social choice and game theory. Click here for syllabus (PDF).

**MAT 102/Mathematics for the Liberal Arts
1 course unit**

(every semester)

A liberal arts course covering topics in modern mathematics. Topics from: logic, sets, combinatorial probability, abstract mathematical systems, and number theory. Click here for syllabus (PDF).

**MAT 105/Mathematical Structures and Algorithms for Educators I
1 course unit**

(every semester)

*: Reserved for School of Education students*

Prerequisite

Prerequisite

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.

This course will be different from other math classes students have taken. In order to support development of problem- solving skills, communication, and mathematical habits of mind, the students will spend the majority of class time working collaboratively, both in groups and as a class presenting ideas and solutions to problems. The instructor’s main role will be to support and facilitate student engagement with and exploration of the material. Click here for syllabus (PDF).

**MAT 106/Mathematical Structures and Algorithms for Educators II
1 course unit**

(every semester)

*: Reserved for School of Education students*

Prerequisite

Prerequisite

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, deaf and hard of hearing, or special education teachers. Click here for syllabus (PDF).

**MAT 111/Number Theory and Systems for Middle School Teachers
1 course unit**

(occasionally)

*Prerequisite*: MAT 105 or MAT 106

This course gives the middle school mathematics teacher a deeper understanding of numbers and operations. Physical materials, models, technology, and middle school curricula will be used to explore these topics. Exploration of ways to engage middle school students meaningfully in experiences that lay a strong foundation for more formal work in number theory will be integrated with the mathematics content. Click here for syllabus (PDF).

**MAT 112/Data Analysis and Problems for Middle School Teachers
1 course unit**

(occasionally)

*Prerequisite*: MAT 105 or MAT 106

This course gives the middle school mathematics teacher a deeper understanding of data analysis and probability. Physical materials, models, technology, and middle school curricula will be used to explore these topics. Exploration of ways to engage middle school students meaningfully in experiences that lay a strong foundation for more formal work in data analysis and probability will be integrated with the mathematics content. Click here for syllabus (PDF).

**MAT 114/Patterns, Functions and Algorithms for Middle School Teachers
1 course unit**

(occasionally)

*Prerequisite*: MAT 105 or MAT 106

This course gives the middle school mathematics teacher a deeper understanding of patterns, functions, and algebra. Physical materials, models, technology, and middle school curricula will be used to explore these topics. Exploration of ways to engage middle school students meaningfully in experiences that lay a strong foundation for more formal algebraic work will be integrated with the mathematics content. Click here for syllabus (PDF).

**MAT 115/Geometry for Middle School Teachers
1 course unit**

(occasionally)

*Prerequisite*: MAT 105 or MAT 106

This course gives the middle school mathematics teacher a deeper understanding of geometry. Physical materials, models, technology, and middle school curricula will be used to explore these topics. Exploration of ways to engage middle school students meaningfully in experiences that lay a strong foundation for more formal work in geometry will be integrated with the mathematics content. Click here for syllabus (PDF).

**MAT 117/Discrete Math for Middle School Teachers
1 course unit**

(occasionally)

*Prerequisite*: MAT 105 or MAT 106

This course gives the middle school mathematics teacher a deeper understanding of discrete mathematics. Physical materials, models, technology, and middle school curricula will be used to explore these topics. Exploration of ways to engage middle school students meaningfully in experiences that lay a strong foundation for more formal work in discrete math will be integrated with the mathematics content. Click here for syllabus (PDF).

**MAT 118/Concepts of Calculus for Middle School Teachers
1 course unit**

(occasionally)

*Prerequisite*: MAT 105 or MAT 106

This course gives the middle school mathematics teacher a deeper understanding of mathematics through the study of calculus. Physical materials, models, technology, and middle school curricula will be used to explore the topics. Exploration of ways to engage middle school students meaningfully in experiences that lay a strong foundation of the ideas of calculus will be integrated with the mathematics content. Click here for syllabus (PDF).

**MAT 119/Introduction to Functions
1 course unit
**(every semester)

*Prerequisite*: MAT 95

Introduction to Functions teaches students the foundational skills needed for success in a Business Calculus course. The course topics include: the fundamentals of algebra, functions, exponential functions, logarithms, and financial models. Stress is on computational and problem-solving techniques. Click here for syllabus (PDF).

**MAT 120/Precalculus
1 course unit**

(every semester)

*Prerequisite*: MAT 95

The Precalculus course teaches students the foundational skills needed for success in a Calculus course. The course topics include: the fundamentals of algebra, exponential functions, logarithms, and trigonometry. Stress is on computational and problem-solving techniques. Click here for syllabus (PDF).

**MAT 125/Calculus for Business and the Social Sciences
1 course unit**

(every semester)

*MAT 119 or MAT 120 or an SAT math score of at least 630 See*

Prerequisite:

Prerequisite:

https://mathstat.tcnj.edu/courses-2/calculus-requirement/ 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. Click here for syllabus (PDF).

**MAT 127/Calculus A
1 course unit**

(every semester)

*MAT 120 or an SAT math score of at least 630 See https://mathstat.tcnj.edu/courses-2/calculus-requirement/ 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. Click here for syllabus (PDF).*

Prerequisite:

Prerequisite:

**MAT 128/Calculus B
1 course unit**

(every semester)

*: MAT 127 or MAT 125 with permission of department chair.*

Prerequisite

Prerequisite

A second course in calculus covering integral calculus and series. The course will cover both the theoretical and applied aspects of calculus. Click here for syllabus (PDF).

**MAT 150/Classical Mathematics of the Mediterranean Region**

**1 course unit**

An introduction to Classical mathematics. Topics may include Mesopotamian computation, Mesopotamian problem tablets, Thales’ geometry, Pythagorean monads, Pythagorean music, ancient number theory, proportions and geometry, the paradoxes of Parmenides and Zeno, geometric construction, geometrical measure, Greek astronomy, Greek trigonometry, Archimedes’ measure and the decline of Greek reasoning. Click here for syllabus (PDF).

**MAT 170/Topics in Mathematics
1 course unit**

(occasionally)

(Special topics in mathematics that will vary by semester.)

**STA 115/Statistics
1 course unit**

(every semester)

This course introduces the students to statistical ideas and concepts with an emphasis on the interpretation of data and the communication of statistical results. Topics include sampling, surveys, experimental designs, observational studies, data exploration, chance phenomena, and methods of statistical inference. Students who have already received credit for STA 215 cannot receive credit for this course. Click here for syllabus (PDF).

## 200-Level Courses

**MAT 200/Proof Writing through Discrete Mathematics
1 course unit**

(every semester)

*MAT 127*

Prerequisite:

Prerequisite:

MAT 200 is primarily an introduction to proof course. It teaches proof using topics from discrete mathematics. It is intended to be first-year course for prospective mathematics majors. It will be scheduled for two 80-minute lecture periods and a 50-minute recitation devoted to proof-writing activities. MAT 127: Calculus A is a prerequisite. Click here for syllabus (PDF).

**MAT 205/Linear Algebra: Theory and Applications
1 course unit**

(every semester)

*: MAT 128 or MAT 200 or CSC 270*

Prerequisite

Prerequisite

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. This course includes a lab component. In this lab, students will learn to use computer software tools such as MATLAB as an aid to solving problems. The use of a computer enables students to tackle more difficult, but more realistic, problems than otherwise possible. Click here for syllabus (PDF).

**MAT 229/Multivariable Calculus
1 course unit**

(every semester)

*MAT 128*

Prerequisite:

Prerequisite:

Topics include: geometry of three dimensional space, derivatives of functions of several variables, integrals in dimension two and three, and Stokes’ theorem. Click here for syllabus (PDF).

**MAT 255/Perspectives on the Development of Mathematics
1 course unit**

(every spring)

*: Reserved for math education students*

Prerequisite

Prerequisite

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. Click here for syllabus (PDF).

**MAT 265/Introduction to Financial Mathematics**

**1 course unit**

(every spring)

*Prerequisite*: MAT 128: Calculus B is the formal prerequisite. An introductory knowledge of probability is also assumed.

MAT 265 will provide students with a sound foundation in both the theoretical and pragmatics aspects of financial mathematics. The course provides an overview of how theoretical concepts and models are used in real-life applications. Students who desire to enter the actuarial or finance professions will be given a solid theoretical understanding of the essential topics in these fields. In addition, this course will cover all of the required topics found on the actuarial FM/2:Financial Mathematics examination. Click here for syllabus (PDF).

**MAT 270/Topics in Mathematics
1 course unit**

(occasionally)

(Special topics in mathematics that will vary by semester.)

**MAT 275/Sophomore Seminar
1/2 course unit**

(every spring)

*Prerequisite:*MAT 200; MAT 205 (prerequisite or corequisite); Mathematics major in their second year of college or have Sophomore standing.

A seminar course designed to help sophomore mathematics and statistics majors develop professionally. Students will work through enriching curriculum modules and challenging stratified problems that may involve discipline specific technological tools. Students will discuss advanced disciplinary texts, career opportunities, internships, and questions of habits of mind and professionalization in mathematics and statistics (with examples including the graduate school application process, potential career progressions, post graduate level work, and issues of diversity and representation inequity in mathematics). Click here for syllabus (PDF).

**MAT 291/Independent Study in Mathematics
variable course units**

(every semester) Click here for syllabus (PDF).

**MAT 292/Guided Study in Mathematics
variable course units**

(every semester) Click here for syllabus (PDF).

**MAT 299/Internship I in Mathematics
variable course units**

(every semester)

*Prerequisite*: Students must have completed a minimum of 4 units at TCNJ. Requires approval of department chair.

A supervised mathematics-related experience in the industrial, governmental, private, or nonprofit sector. Click here for syllabus (PDF).

**MTT 202/Teaching Mathematics in the Early Childhood and Elementary Classroom
1 course unit**

(with field placement)

(every semester)

*: MAT 105, MAT 106, or by permission of Math. Ed. coordinator*

Prerequisite

Prerequisite

*: MST 202*

Corequisite

Corequisite

This course examines the early childhood and elementary 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-5 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 3 hours per week. Click here for syllabus (PDF).

**MTT 299/Internship I in Mathematics Education
variable course units**

(every semester)

*Prerequisite*: Students must have completed a minimum of 4 units at TCNJ. Requires approval of department chair.

A supervised mathematics education related experience in the industrial, governmental, private, or nonprofit sector.

Click here for syllabus (PDF).

**STA 215/Statistical Inference & Probability
1 course unit**

(every semester)

Prerequisite

Prerequisite

*or corequisite*: MAT 125 or MAT 127

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. Because many of the analysis techniques require extensive computations, for other than the simplest data sets, each student will become familiar with one or more of the software packages (e.g., Minitab, SPSS, Excel, etc.) or other tools, such as a graphing calculator, that are available. Click here for syllabus (PDF).

**STA 216/Statistical Inference & Probability for Educators
1 course unit**

(every fall)

*: MAT 125 or MAT 127*

Prerequisite or corequisite

Prerequisite or corequisite

This course introduces future mathematics educators to statistical ideas and concepts with an emphasis on methods of statistical inference (notably confidence intervals and hypothesis tests) and probability (notably conditional probability, the binomial distribution, and concepts relating to independence and disjoint probabilities). Click here for syllabus (PDF).

**STA 291/Independent Study in Statistics
variable course units**

(every semester) Click here for syllabus (PDF)

**STA 292/Guided Study in Statistics
variable course units**

(every semester) Click here for syllabus (PDF)

**STA 299/Internship I in Statistics
variable course units**

(every semester)

*Prerequisite*: Students must have completed a minimum of 4 units at TCNJ. Requires approval of department chair.

A supervised statistics-related experience in the industrial, governmental, private, or nonprofit sector.

Click here for syllabus (PDF).

## 300-Level Courses

**MAT 301/Number Theory
1 course unit**

(every semester)

*MAT 200*

Prerequisite:

Prerequisite:

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. Click here for syllabus (PDF).

**MAT 303/Cryptography and Coding Theory
1 course unit**

(occasionally)

*MAT 200 and MAT 205*

Prerequisites:

Prerequisites:

A survey of the fields of cryptography and coding theory. Topics will be chosen from the fields of historical cryptography, public key-cryptography, Diffie-Hellman, ElGamal, elliptic curve cryptography, elliptic curve factoring, hash functions, and error-correcting codes (Hamming codes, BCH codes, Reed-Solomon, algebraic geometric codes). Click here for syllabus (PDF).

**MAT 305/Abstract Algebra
1 course unit**

(every semester)

*MAT 200 and MAT 205*

Prerequisites:

Prerequisites:

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. Click here for syllabus (PDF).

**MAT 310/Real Analysis
1 course unit**

(every semester)

*: MAT 200 and MAT 229*

Prerequisites

Prerequisites

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. Click here for syllabus (PDF).

**MAT 315/Topics in Linear Algebra
1 course unit**

(occasionally)

*MAT 205*

Prerequisite:

Prerequisite:

The course consists of a collection of topics not covered in MAT 205 and builds 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. Click here for syllabus (PDF).

**MAT 316/Probability
1 course unit**

(every fall)

*MAT 200*

Prerequisites:

Prerequisites:

*Prerequisite or corequisite:*MAT 229

An introduction to probability. Topics include mathematical models, sample spaces, conditional probability, discrete and continuous distributions, expected values, moment-generating functions, Central Limit Theorem, multivariate distributions, marginal distributions, conditional distributions, correlation, and one-variable transformations of variables. Click here for syllabus (PDF).

**MAT 317/Linear Programming
1 course unit**

(occasionally)

*: MAT 127 or MAT 125, and MAT 205*

Prerequisites

Prerequisites

The course studies the optimization of linear functions with constraints. Its methods are widely used in mathematical modeling. The course provides an introduction to the algorithms, theoretical foundations, and applications of linear programming. Selected topics include: the simplex method for solving a linear program (LP), the geometry of LPs, variants of the simplex method, constructing mathematical models using LPs, duality theory, sensitivity analysis, integer programming, transportation and trans-shipment models, network models, program management models, and solving LPs using modern software packages. Click here for syllabus (PDF).

**MAT 320/Complex Analysis
1 course unit**

(occasionally)

*MAT 229*

Prerequisite:

Prerequisite:

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. Click here for syllabus (PDF).

**MAT 326/Differential Equations
1 course unit**

(every semester)

*MAT 128 and*

Prerequisite:

Prerequisite:

*Corequisite:*MAT 205 or PHY 306

The subject of Differential Equations is the study of deterministic models of nature and historically it was developed principally for study of problems of physics. Now, however, differential equations have a much broader application to chemistry, biology and the social sciences. Differential Equations is one of the foundational topics in the modern- day study of dynamical systems. Students will draw upon their knowledge of calculus and linear algebra in formulating their solutions to many types of differential equations. Click here for syllabus (PDF)

** MAT 330/BIO 330/Mathematical Biology
1 course unit
**(Every other year, usually fall)

*MAT 128 is a prerequisite, and MAT 205 is a corequisite. An interest in biology is recommended for MAT 330. MAT 128 and BIO 201 are prerequisites for BIO 330.*

Prerequisites:

Prerequisites:

In this course, we will focus on building and analyzing dynamic mathematical models (models that study how processes change in time) to understand the behavior of different biological systems. This course will focus on a variety of topics in population biology, physiology and the biomedical sciences such as single and competing species models, pharmacokinetic models of drugs and toxins, enzyme reaction kinetics, epidemiology, infectious diseases and cancer. We will use mathematical tools like difference equations, differential equations, linear algebra and nonlinear analysis to study these biological processes. Further, computer software packages, such as MATLAB, will be used to implement these mathematical models in search of answers to biological questions. When possible, numerical simulations of the models will be run in MATLAB to compare model outputs to experimental data. Click here for syllabus (PDF).

**MAT 331/Numerical Analysis
1 course unit**

(Every other year, usually fall)

*MAT 128 and MAT 205*

Prerequisites:

Prerequisites:

Numerical Methods is a course which focuses on methods of approximating solutions to problems for which the techniques of the earlier Calculus and Linear Algebra courses fail. A course covering methods of approximation, errors in approximation, and efficiency of algorithms.Click here for syllabus (PDF).

**MAT 341/Computational Mathematics**

**1 course unit**

*Prerequisites: *MAT 200, MAT 205, and CSC 220 or CSC 250

Computational Mathematics combines the beauty and logic of mathematics with computing. In Computational Mathematics, students will learn how to develop and implement mathematical algorithms that can be utilized to solve real-world problems across many disciplines. Much of the course content will draw on topics from earlier mathematics courses, but these topics will be covered from a computer solution point of view. Click here for syllabus (PDF).

**MAT 351/Geometry
1 course unit**

(every semester)

*MAT 200 and MAT 229*

Prerequisites:

Prerequisites:

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. Click here for syllabus (PDF).

**MAT 370/Topics in Mathematics
1 course unit**

(occasionally)

(Special topics in mathematics that will vary by semester.)

**MAT 391/Independent Study in Mathematics
variable course units**

(every semester) Click here for syllabus (PDF).

**MAT 392/Guided Study in Mathematics
variable course units**

(every semester) Click here for syllabus (PDF).

**MAT 393/Independent Research in Mathematics
variable course units**

(every semester)

*By invitation only*

Prerequisite:

Prerequisite:

Student will study and/or do research independently in an appropriate area. A department member will be assigned to advise and direct the student. Click here for syllabus (PDF).

**MAT 399/Internship II in Mathematics
variable course units**

(every semester)

*Prerequisite*: Students must have completed a minimum of 4 units at TCNJ. Requires approval of department chair.

A supervised mathematics-related experience in the industrial, governmental, private, or nonprofit sector.

Prerequisite: Students must have completed a minimum of 4 units at TCNJ. Requires approval of department chair. A supervised statistics-related experience in the industrial, governmental, private, or nonprofit sector. Click here for syllabus (PDF).

**MTT 300/Learning Assistant in Mathematics Education
1 course unit
**(every semester)

*Prerequisite*: Department permission.

A student enrolled in this course serves as a Learning Assistant in a single course under the supervision of a professor. Learning Assistants gain experience in teaching through supervised activities such as assisting students with classroom activities, holding office hours, leading discussions, and holding review sessions. Learning Assistants meet with the supervising professor regularly to discuss course content, pedagogy, and performance. Learning Assistants are assessed based on their work in and out of the classroom and on a final, reflective paper in which they discuss their experiences in this role. Click here for syllabus (PDF).

**MTT 370/Special Topics in Mathematics Education
.5 course unit**

(occasionally)

*Prerequisite*: MAT 105 or MAT 200 are a prerequisite.

This course covers a variety of topics in Mathematics Education.

**MTT 380/Methods of Teaching Mathematics I
1 course unit**

(fall)

*MAT 200, MAT 205, and MAT 229*

Prerequisites:

Prerequisites:

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 will include the use of manipulatives, technology in teaching mathematics and the investigation of standards-based curricula. These topics will be mostly situated in the context of middle school mathematics. Click here for syllabus (PDF).

This is a writing intensive course.

**MTT 390/Methods of Teaching Mathematics II
1 course unit**

(spring)

*MTT 380*

Prerequisites:

Prerequisites:

*SED 399 and SPE 323*

Corequisites:

Corequisites:

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 Clinical Practice I. Click here for syllabus (PDF).

**MTT 391/Independent Study in Mathematics Education
variable course units**

(every semester)

This course is an upper level course for students interested in studying topics that are not covered in the regularly offered courses. To register for the course a student must contact a faculty member of the department who will serve as a mentor of the independent study. Students must have completed either MTT 202 or MTT 380 with at least a grade of B to register for the course. .

Click here for syllabus (PDF).

**MTT 392/Guided Study in Mathematics Education
variable course units**

(every semester)

This course is an upper level course for students interested in studying topics that are not covered in the regularly offered courses. Students must have completed either MTT 202 or MTT 380 with at least a grade of B to register for the course. Click here for syllabus (PDF).

**MTT 393/Independent Research in Mathematics Education
variable course units**

(every semester)

This course is an upper level course in which students engage in research experiences in mathematics education that constitute new research for the student. Students work in collaboration with a faculty member and/or with fellow student researchers and a faculty mentor. The student will be expected at the end of the semester to write a paper which will be presented to the department or at a mathematics education conference. To register for the course a student must make arrangements with a faculty member of the department who agrees to serve as a research mentor. Students must have completed either MTT 202 or MTT 380 with at least a B to register for the course. Click here for syllabus (PDF).

**STA 303/Design of Experiments
1 course unit**

(every other fall)

*: STA 215*

Prerequisites

Prerequisites

An introduction 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). Click here for syllabus (PDF).

**STA 304/Sampling and Nonparametric Statistics
1 course unit**

(every other fall)

*: STA 215*

Prerequisites

Prerequisites

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. Click here for syllabus (PDF).

**STA 305/Regression Analysis
1 course unit**

(every fall)

*: STA 215*

Prerequisites

Prerequisites

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 and time series analysis. A statistical software package will be used throughout the course (SAS, SPSS, or MINITAB). Click here for syllabus (PDF).

**STA 306/Applied Multivariate Analysis
1 course unit**

(every spring)

*: STA 215*

Prerequisites

Prerequisites

An introduction 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). Click here for syllabus (PDF).

**STA 307/Data Mining and Predictive Modeling
1 course unit**

(spring of even years)

*: (CSC 220 or CRI 215) and STA 215*

Prerequisites

Prerequisites

An introduction to data mining, focusing on classification and clustering. Classification topics include traditional statistical classifiers and new computational methods, such as random forests and support vector machines. Clustering topics include the use of different methods, metrics, and ensembles.Click here for syllabus (PDF).

**STA 314/Statistical Quality Control
1 course unit**

(occasionally)

*: STA 215*

Prerequisites

Prerequisites

Course description: An introduction to the theory and application of statistical quality control. Topics include variables control charts (, R, and s), attributes control charts (p, np, c, and u), and non-Shewhart type charts (CUSUM, MA, and EWMA); rational subgrouping, Average Run Length, and O-C curves. Click here for syllabus (PDF).

**STA 318/Operations Research
1 course unit**

(fall odd years)

*: MAT 316*

Prerequisite

Prerequisite

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. Click here for syllabus (PDF).

**STA 390/Statistics Specific Research Course
variable course units
**(every semester)

**STA 391/Independent Study in Statistics
variable course units**

(every semester) Click here for syllabus (PDF).

**STA 392/Guided Study in Statistics
variable course units**

(every semester) Click here for syllabus (PDF)

**STA 393/Independent Research in Statistics
variable course units**

(every semester)

*By invitation only*

Prerequisite:

Prerequisite:

Student will study and/or do research independently in an appropriate area. A department member will be assigned to advise and direct the student. Click here for syllabus (PDF)

**STA 399/Internship II in Statistics
variable course units**

(every semester)

*Prerequisite*: Students must have completed a minimum of 4 units at TCNJ. Requires approval of department chair.

A supervised statistics-related experience in the industrial, governmental, private, or nonprofit sector.

Prerequisite: Students must have completed a minimum of 4 units at TCNJ. Requires approval of department chair. A supervised statistics-related experience in the industrial, governmental, private, or nonprofit sector. Click here for syllabus (PDF).

## 400-Level Courses

**MAT 403/Advanced Calculus with Topology
1 course unit**

(Occasionally)

*: MAT 229 and MAT 205 OR PHY 306 and a 300-level Math course.*

Prerequisite

Prerequisite

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). Click here for syllabus (PDF).

**MAT 405/Topology
1 course unit**

(occasionally)

*MAT 305*

Prerequisite:

Prerequisite:

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. Click here for syllabus (PDF).

**MAT 407/Projective Geometry
1 course unit**

(occasionally)

*MAT 305*

Prerequisite:

Prerequisite:

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. Click here for syllabus (PDF).

**MAT 426/Partial Differential Equations
1 course unit**

(every other fall — (expected))

*MAT 326*

Prerequisite:

Prerequisite:

The course is a mixture of theory and computation, with a focus on orthogonal functions and the associated classical theory. It begins with the study of the standard methods for determining solutions to the classic equations from physics using Fourier Series and transform methods, and ends with more general equations where numerical approximations of solutions will be necessary. Click here for syllabus (PDF).

**MAT 430/Seminar in Dynamical Systems
1 course unit**

(occasionally)

*MAT 326*

Prerequisites:

Prerequisites:

This course is an introduction to the study of systems whose states change over time – such systems are called dynamical systems. The subject of dynamical systems lies at the border of pure and applied mathematics, with concepts from many areas of theoretical mathematics (analysis, linear algebra, etc.) being used to study these systems as they arise in a broad range of fields, including physics, biology and chemistry. Three main types of dynamical systems will be studied in this class: discrete-time one dimensional maps, continuous-time one dimensional flows on lines and circles, and continuous-time two dimensional linear and nonlinear flows. Click here for syllabus (PDF).

**MAT 440/Mathematical Logic
1 course unit**

(occasionally)

*MAT 200, a 300-level MAT course and reserved for juniors and seniors*

Prerequisites:

Prerequisites:

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. Click here for syllabus (PDF).

**MAT 451/Seminar in Algebra
1 course unit**

(occasionally)

*MAT 229 and MAT 305*

Prerequisites:

Prerequisites:

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. Click here for syllabus (PDF).

**MAT 452/Seminar in Geometry and Topology
1 course unit**

(occasionally)

*: MAT 229 and MAT 305*

Prerequisites

Prerequisites

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. Click here for syllabus (PDF).

**MAT 453/Seminar in Analysis
1 course unit**

(occasionally)

*: MAT 229 and MAT 310*

Prerequisites

Prerequisites

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. Click here for syllabus (PDF).

**MAT 454/Seminar in Applied Mathematics
1 course unit**

(every fall)

*Prerequisites:*MAT 229 and MAT 326

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 students as well as to bridge the gap between undergraduate math and graduate math. Click here for syllabus (PDF).

**MAT 470/Topics in Mathematics
1 course unit**

(occasionally)

(Special topics in mathematics that will vary by semester.)

**MAT 492/Guided Study in Mathematics II
variable course units**

(every semester)

This course allows student to study advanced mathematical topics under the supervision of a faculty member. Click here for syllabus (PDF).

**MAT 493/Independent Research II in Mathematics
variable course units**

(every semester)

*By invitation only*

Prerequisite:

Prerequisite:

Student will study and or do research independently in an appropriate area. A department member will be assigned to advise and direct the student. Click here for syllabus (PDF).

**MAT 494/Independent Study in Mathematics II
variable course units**

(every semester)

The course allows students to study advanced mathematical topics independently under the supervision of a faculty member. Click here for syllabus (PDF).

**MAT 497/Topics in Secondary Mathematics from an Advanced Viewpoint**

*Prerequisite: *MTT 380, MAT 305, MAT 351, and at least one other 300-level course.

In MAT 497, teacher candidates will build on what they have learned in their undergraduate mathematics courses, MTT 380, and MTT 390 to explore the inherent coherence of the mathematics of high school and middle school and the structure of mathematical ideas from which the high school and middle school curriculum is derived. Prospective teachers will examine connections between middle school and high school mathematics as well as connections between high school and college mathematics. A teacher who is aware of and understands these connections will be better prepared to teach in a manner consistent with state and national Standards. Click here for syllabus (PDF).

**MAT 498/Capstone **

(every spring)

*Course prerequisites*: Senior standing – the Capstone is to be taken in a student’s last or penultimate semester at TCNJ. Prerequisites for individual specializations are detailed below.

*Applied Mathematics*: MAT 310, MAT 326, CSC 220 or CSC 250, and two mathematics/statistics options at the 300/400 level. Corequisite: two additional mathematics/statistics options at the 300/400 level. At most three of the four options can be STA courses.

*Mathematics*: MAT305, MAT310, and two mathematics options at the 300-level or above, at least one of these at the 400-level or above. Corequisite: two additional mathematics options at the 300-level or above.

Intensive study of advanced topics in mathematics. Students will write and present an expository paper in mathematics. Click here for syllabus (PDF).

**MTT 490/Clinical Practice II
2 course units**

(every semester)

*MTT 390 and meeting all the criteria for admission for student teaching including completion of STA 216, MAT 301, MAT 351, and MAT 305, and all but at most 3 of their required mathematics courses, at least C+ in MTT 390, and cumulative average of at least 3.0.*

Prerequisites:

Prerequisites:

*SED 498*

Corequisite:

Corequisite:

Student Teaching during the senior year under direct supervision of approved public school and general supervision of college supervisors. Observation, participation, and responsible teaching. Click here for syllabus (PDF).

**MTT 491/Global Student Teaching
2 course units**

(every semester)

*MTT 390 and meeting all the criteria for admission for student teaching including completion of STA 216, MAT 301, MAT 351, and MAT 305, and all but at most 3 of their required mathematics courses, at least C+ in MTT 390, and cumulative average of at least 3.0.*

Prerequisites:

Prerequisites:

*SED 498*

Corequisite:

Corequisite:

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. Click here for syllabus (PDF).

**MTT 493/Independent Research in Mathematics Education II
variable course units**

(every semester by invitation only)

*MTT 202 or MTT 380 and overall GPA of at least 3.0.*

Prerequisites:

Prerequisites:

This course is an upper level course in which students engage in research experiences on advanced mathematics education topics that constitute new research for the student. Students work in collaboration with a faculty member and/or with fellow student researchers and a faculty mentor. The student will be expected at the end of the semester to write a paper which will be presented to the department or at a mathematics education conference. To register for the course a student must make arrangements with a faculty member of the department who agrees to serve as a mentor of the independent research. Students can register for the course by invitation only and must have passed MTT 202 or MTT 380 with at least a B and have an overall GPA of at least 3.0. Click here for syllabus (PDF).

**STA 404/Computational and Bayesian Statistics
1 course unit
**(every odd spring)

*: STA 305, CSC 230 OR CSC 250 OR CRI 215, MAT 205.*

Prerequisites

Prerequisites

This course will present an introduction to computational and Bayesian statistics. Topics include Bayesian computational methods, including the effect of prior knowledge in estimation and setting of confidence intervals, and the impact of computational methods on non-Bayesian methods. Substantial statistical programming will be involved. Click here for syllabus (PDF)

**.**

**STA 410/Mathematical Statistics**

1 course unit

(every spring)*.
Prerequisites*: STA 115 or STA 215, and MAT 316

An introduction to the theory of statistics. Topics include transformations of variables; sampling distributions of common statistics; method of moments and maximum likelihood estimation; properties of point estimates including bias, MSE, consistency, and sufficiency; confidence intervals; and hypothesis testing, including Type I and II Errors and power. Click here for syllabus (PDF)

**STA 492/Guided Study in Statistics II
variable course units**

(every semester)

STA 492 is an upper level course in statistics for students interested in studying topics that are not covered in the regularly offered statistics courses. The course is given as a group study course. A small group of students agrees to take the course and work together during the semester on a specific topic. To register for the course, students must make arrangements with a faculty member of the department who agrees to serve as a mentor for the guided study. Students must have a 3.0 GPA in their mathematics and statistics courses to register for the course. Click here for syllabus (PDF).

**STA 493/Independent Research II in Statistics
variable course units**

(every semester)

*MAT 316 and at least one 300-level Statistics course*

Prerequisite:

Prerequisite:

STA 493: “Independent Research II in Statistics” is an upper level course for majors in their Senior year who have at least a 3.5 GPA. Its prerequisites are MAT 316 and at least one 300-level Statistics course. It also has STA 410 as a prerequisite or corequisite course. The student should develop the topic for the research with a faculty member. Although it is typical that this topic would be in the area of research for the faculty member, this is not required. Click here for syllabus (PDF).

**STA 494/Seminar in Statistics
1 course unit**

(occasionally)

*STA 215*

Prerequisite:

Prerequisite:

A flexible course in which the content is selected from topics in statistics. This is an elective course designed to enrich the background of the students as well as to bridge the gap between undergraduate statistics and graduate statistics. Click here for syllabus (PDF).

**STA 498/Capstone **

(every spring)

*Prerequisites*: Senior standing – the Capstone is to be taken in a student’s last or penultimate semester at TCNJ. MAT 316 and 2 additional 300-level courses are prerequisites.

*Corequisite: *STA 410

Intensive study of topics or applications in statistics. Verbal presentation and written paper required. Click here for syllabus (PDF).

## 500-Level Courses

**MAT 502/Guided Study in Mathematics
1 course unit**

(occasionally)

*Students should have taken at least two 400-level MAT courses and have at least a 3.5*

Prerequisite:

Prerequisite:

GPA in their math courses.

A graduate level course for students interested in studying advanced mathematical topics that are not covered in the undergraduate courses offered in the department. To register for the course, students must make arrangements with a faculty member of the department who agrees to serve as a mentor for the guided study. Students must have taken at least two 400-level MAT courses and have at least a 3.5 GPA in their math courses to register for the course. Click here for syllabus (PDF).