Syllabus

This introductory course will create a foundational understanding of topics in Algebra. An emphasis will be on applications to prepare students for future courses like Precalculus or Statistics. After a review of elementary algebra concepts, topics covered include: equations and inequalities, linear equations, exponents and polynomials, factoring, rational expressions and equations, relations and functions, radicals, linear and quadratic equations, higher-degree polynomials, exponential, logarithmic, and rational functions.
Prerequisite: None.
Credits: 4 credits
Required Text: College Algebra, by Larson, 11th Edition. Online Homework Platform⁠—WebAssign ISBN-13: 9780357454404

Note: This textbook is offered through WebAssign to pair with the online assignments. It includes seamless access to the eBook as well as study tools to use throughout the course⁠. If you would like to purchase a physical copy of the textbook you are more than welcome to do so, however WebAssign access is still required.

Syllabus

This course provides students with the background necessary for the study of calculus. It begins with a review of the coordinate plane, linear equations, and inequalities, and moves purposefully into the study of functions. Students will explore the nature of graphs and deepen their understanding of polynomial, rational, trigonometric, exponential, and logarithmic functions, and will be introduced to complex numbers, parametric equations, and the difference quotient.
Prerequisite: None.
Credits: 4 credits
Required Text: PreCalculus, by Faires and DeFranza., 5th Ed., ISBN-13: 978-0-84006862-0 ISBN-10: 0-8400-6862-X

Syllabus

This is a second course in the calculus of functions of one independent variable. However, instead of continuing with standard calculus topics, this semester includes an introduction to differential equations, the basic structure of functions of several variables, an introduction to linear systems and linear algebra, and applications for systems of linear differential equations and probability distributions. Applications to the biological and social sciences will be discussed, and the course is designed to meet the needs of students in these disciplines.
This course is part of a two course sequence and succeeds AS.110.106 Calculus I (Biology and the Social Sciences). Students planning to take this course must demonstrate a proficiency in some form of first semester university calculus, either through the AP system resulting with an AB score of 5 or a BC score of 3 or better, or a course like AS.110.106 Calculus I. It is possible to gain access to this course via an adequate score on the Placement Exam II offered by the Mathematics Department, but that also requires permission form the department. This sequence of courses are considered terminal and are typically not to be considered adequate preparation for higher mathematics. This sequence satisfies a core requirement of two semesters of single variable calculus for both the major and minor in mathematics.
Credits: 4 credits
Required Text:  Calculus for Biology and Medicine, 4^th Edition, C. Neuhauser and M. Roper, New Jersey: Prentice Hall, January 2018, ISBN-10: 0134070046, ISBN-13: 978-0134070049

Syllabus

This is the first of a two course sequence in the differential and integral calculus of single variable functions. Topics include the basic analytic geometry of graphs of functions, and their limits, integrals and derivatives, including the Fundamental Theorem of Calculus. Also, some applications of the integral, like arc length and volumes of solids with rotational symmetry, are discussed. Applications to the physical sciences and engineering will be a focus of this course, as this sequence of courses is designed to meet the needs of students in these disciplines. 4 credits

The calculus course sequence is considered foundational to all higher-level courses in mathematics. This course satisfies the core requirement for the first of two semesters of single variable calculus for both the major and minor in mathematics.

Prerequisite: Students planning to take this course must demonstrate a proficiency in pre-calculus, either through the successful completion of a prior course in pre-calculus (such as AS.110.105 or similar) or by achieving an adequate score in the Placement Exam I offered by the Mathematics Department.

Credits: 4 credits
Required Text: Single Variable Calculus: Early Transcendentals, by James Stewart, 8th Ed., ISBN: 978-1-305-27033-6.

Syllabus

This is the second of a two course sequence in the differential and integral calculus of single variable functions. Topics include techniques of integration, applications of integrals, polar coordinates, parametric equations, Taylor’s theorem and applications, infinite sequences and series. Some applications to the physical sciences and engineering will be discussed, as this sequence of courses are designed to meet the needs of students in these disciplines. 4 credits

Prerequisite: Successful completion of AP Calculus AB, Calculus I, or equivalent.
Credits: 4 credits
Required Text: Single Variable Calculus: Early Transcendentals, by James Stewart, 8th Ed., ISBN: 978-1-305-27033-6.

As artificial intelligence models like ChatGPT and Claude become increasingly sophisticated, understanding how they work is more important than ever. This course introduces students to the mathematical and statistical principles behind machine learning and AI technologies. Students will learn the mathematical concepts behind classification and prediction models and implement these models in Python. Working with real-world data, students will design machine learning applications that power modern AI systems. Models studied include linear regression, classification trees, neural networks, and K-nearest neighbors (KNN). By testing and improving their models, students will gain insight into both the possibilities and limitations of AI.

Prerequisites: High School Algebra 1
Credits: 1 credits
Required Text: None

Syllabus

This online course introduces students to important concepts in data analytics across a wide range of case studies. Students will learn how to gather, analyze, and interpret data to drive strategic and operational success. They will explore how to clean and organize data for analysis, and how to perform calculations using Microsoft Excel. Topics include the data science lifecycle, probability, statistics, hypothesis testing, set theory, graphing, regression, and data ethics.

Prerequisites: None
Credits: 4 credits
Required Text: None

Mathematics for Sustainability covers topics in measurement, probability, statistics, dynamics, and data analysis. In this course, students will analyze, visually represent, and interpret large, real data sets from a variety of government, corporate, and non-profit sources. Through local and global case studies, students will engage in the mathematics behind environmental sustainability issues and the debates centered on them. Topics include climate change, natural resource use, waste production, air and water pollution, water scarcity, and decreasing biodiversity. The software package R is used throughout the semester.

Prerequisites: Comfort with algebraic expressions and functions. No prior experience in coding is required.
Credits: 4 credits
Required Text: Mathematics for Sustainability, Roe, DeForest, JamShidi

Syllabus

This course is an introduction to the techniques of linear algebra in Euclidean space. Topics covered include matrices, determinants, systems of linear equations, vector spaces, linear transformations, complex numbers, and eigenvalues and eigenvectors. Diagonalization of matrices and quadratic forms, as well as applications of these topics to the biological, physical and social sciences to are also included.
Prerequisite: Successful completion of Calculus I. Recommended: Calculus II.
Credits: 4 credits
Required text: Linear Algebra with Applications by Bretscher, Prentice, 5th Edition, ISBN9780321796974

Syllabus

List of Topics by Week

This is a course in the differential and integral calculus of several variables. Topics include vectors in two and three dimensions, analytic geometry of three dimensions, parametric curves, partial derivatives, the gradient, optimization in several variables, multiple integration with change of variables across different coordinate systems, line integrals, surface integrals, and Green’s Theorem, Stokes’ Theorem, and Gauss’ Divergence Theorem.
Prerequisite: Successful completion of AP Calculus BC, Calculus II, or equivalent.
Credits: 4 credits
Required text: Vector Calculus by Marsden & Tromba, Freeman, 6th Ed., ISBN 9781429215084

Syllabus

This course provides a rigorous yet accessible introduction to the essential mathematical foundations underlying modern Artificial Intelligence (AI) and Deep Learning applications. The course emphasizes the practical application of linear algebra, probability, statistics, calculus, and optimization techniques in the design and understanding of machine learning systems. Students will explore how these core mathematical tools are used to build models for computer vision, regression, classification, clustering, and deep neural networks. Each topic is contextualized with real-world problems, Python Code, and bridging theory with implementation. The course is designed for students from diverse academic backgrounds who want to gain a solid foundation in mathematics for working with AI systems. Topics include: Vectors, matrices, and tensor operations; Calculus and gradient-based optimization for training neural networks; Probability theory and statistical inference in machine learning; Mathematical intuition behind computer vision, regression, classification, clustering, and deep neural networks with practical use cases.

Prerequisite: Precalculus (AS.110.105 or similar)
Credits: 4 credits
Required text: Practical Mathematics for AI and Deep Learning: A Concise yet In-Depth Guide on Fundamentals of Computer Vision, NLP, Complex Deep Neural Networks and Machine Learning by Gosh and Belagal

Syllabus

This course is designed for students of all backgrounds to provide a solid foundation in the underlying mathematical, programming, and statistical theory of data analysis. In today’s data driven world, data literacy is an increasingly important skill to master. To this end, the course will motivate the fundamental concepts used in this growing field. While discussing the general theory behind common methods of data science there will be numerous applications to real world data sets. In particular, the course will use Python libraries to create, import, and analyze data sets.

Prerequisite: None
Credits: 4 credits
Required (free) text: Introduction to Statistical Learning by James, Witten, Hastie, Tibshirani

This course introduces students from all disciplines to the principles and practices of calculus-based statistics as a tool for understanding civic life. The course integrates foundational concepts from probability theory with statistical inference, emphasizing how probabilistic models underpin the construction of confidence intervals and hypothesis tests. Students develop fluency in describing, interpreting, and critically evaluating quantitative information found in public discourse, including polls, media reports, policy analyses, and scientific studies. Through a combination of theoretical development and hands-on data analysis, students learn to compute and interpret confidence intervals, conduct hypothesis tests, and assess uncertainty using probabilistic reasoning. Real-world case studies are used to connect formal statistical methods to questions arising in democratic society. Students will use R and other relevant software (e.g., Python) to analyze datasets, simulate probabilistic models, and communicate evidence-based conclusions.

Prerequisites: Precalculus
Credits: 4 credits
Required text: TBD

Syllabus

This course follows the actuarial Exam P syllabus and learning objectives to prepare students to pass the SOA/CAS Probability Exam. Topics include axioms of probability, discrete and continuous random variables, conditional probability, Bayes’ theorem, Chebyshev’s Theorem, Central Limit Theorem, univariate and joint distributions and expectations, transformations of random variables and moment generating functions. Exam P learning objectives and learning outcomes are emphasized.

Prerequisite: Calculus II.
Credits: 4 credits
Required text:  Probability and Statistical Inference by Hogg, Tanis, and Zimmerman, 10th edition, ISBN 9780135189399

Syllabus

This course is designed to develop students’ understanding of fundamental concepts of financial mathematics. The course will cover mathematical theory and applications including the time value of money, annuities and cash flows, bond pricing, loans, amortization, stock and portfolio pricing, immunization of portfolios, swaps and determinants of interest rates, asset matching and convexity. A basic knowledge of calculus and an introductory knowledge of probability is assumed.

Prerequisite: Calculus I or equivalent.

Credits: 4 credits
Required text:  Interest Theory: Financial Mathematics and Deterministic Asset Valuation by Francis and Ruckman. ISBN-13: 978-0998160405

Syllabus

This course will provide a practical introduction to mathematical proof, both as they have been done for centuries, and using a modern technological theorem prover. The course begins with the basic building blocks of mathematics: propositional logic, set theory, functions, and relations. These foundational tools lead to answers to questions that are surprisingly difficult, like “what are numbers?” Students will be exposed to mathematical notation and how to create it in digital documents, as well as an “artificially intelligent” proof assistant. The course will conclude with a consideration of the role of A.I. in pure mathematics, particularly as it applies to proofs.

Prerequisite: None.
Credits: 4 credits

Syllabus

List of Topics by Week

This is an applied course in ordinary differential equations, which is primarily for students in the biological, physical and social sciences, and engineering. Techniques for solving ordinary differential equations are studied. Topics covered include first order differential equations, second order linear differential equations, applications to electric circuits, oscillation of solutions, systems of linear differential equations, autonomous systems, Laplace transforms and linear differential equations, mathematical models (e.g., in the sciences or economics).
Prerequisite: Calculus II.
Credits: 4 credits
Required text: Elementary Diff Equations & Boundary Value Problems by Boyce & DiPrima, Wiley, 10th edition, ISBN 9780470458310

Syllabus

This course is designed for students of all backgrounds to provide a mathematical introduction to social choice theory, weighted voting systems, apportionment methods, and gerrymandering. In the search for ideal ways to make certain kinds of political decisions, a lot of wasted effort could be averted if mathematics could determine that finding such an ideal were actually possible in the first place.

The course will analyze data from recent US elections as well as provide historical context to modern discussions in politics, culminating in a mathematical analysis of the US Electoral College. Case studies, future implications, and comparisons to other governing bodies outside the US will be used to apply the theory of the course. Students will use Microsoft Excel to analyze data sets. There are no mathematical prerequisites for this course.

Credits: 4 credits

Syllabus

This course offers an introduction to elementary number theory with minimal background prerequisites. Following Silverman’s Friendly Introduction to Number Theory, we will cover essential concepts and some of the most celebrated results in elementary number theory, including Pythagorean triples, divisibility, the theorems of Fermat, Euler, and Wilson, the Chinese remainder theorem, prime numbers and factorization, some arithmetic functions, primitive roots, quadratic reciprocity, sums of two squares, and Diophantine equations. Time permitting, additional topics from later chapters in the book, such as Pell’s equation, continued fractions, or factorization in the Gaussian integers, may also be included.
Prerequisite: Calculus II or equivalent.
Credits: 4 credits
Required Text: A Friendly Introduction to Number Theory – Joseph H. Silverman, 4th ed., ISBN 9780321816191

Syllabus

This course is an introduction to the theory of functions of one complex variable. Its emphasis is on techniques and applications, and it serves as a basis for more advanced courses. Topics include functions of a complex variable and their derivatives; power series and Laurent expansions; the Cauchy integral theorem and formula; calculus of residues and contour integrals; harmonic functions.
Prerequisite: Linear Algebra and Calculus III.
Credits: 4 credits
Required text: Fundamentals of Complex Analysis (with Applications to Engineering and Science), 3^rd Edition, E. B. Saff & A. D. Snider. Prentice Hall, January 2003, ISBN-10: 0139078746, ISBN-13: 978-0139078743

This is a course in discrete mathematics that will introduce students to combinatorics, graph theory and optimization, with an emphasis on techniques of enumeration. This course will introduce the art of counting and the utility of representing objects as graphs. In particular, this course will focus on Enumeration Techniques = formalizing and developing techniques to count certain sets of objects using bijective proofs, generating functions, and the Principle of Inclusion/Exclusion; basics of graphs – defining graphs and investigating some of their properties such as existence of matchings and optimized matching algorithms, colorability, and topological embeddings; and applications of graphs in other areas of math and science such as probability, electrical networks, group theory and cryptography.

Prerequisites: Basic knowledge of calculus and linear algebra and general comfort writing and understanding proofs.
Credits: 4 credits
Required texts: None. Selected readings from free online sources will be provided in the course.

Syllabus

The Mathematics of Cryptography and Cybersecurity introduces students to the mathematical principles that secure digital communication in the modern world. The course focuses on the theory and construction of public-key cryptosystems and digital signature schemes, emphasizing the number-theoretic foundations of data security. Students will explore how mathematical ideas such as modular arithmetic, prime factorization, and discrete logarithms underpin real-world cybersecurity protocols including RSA, Diffie–Hellman key exchange, and elliptic curve cryptography.

In addition to classical and modern cryptographic systems, the course highlights the role of mathematics in assessing vulnerabilities, analyzing security guarantees, and understanding emerging cryptographic challenges in cybersecurity. Topics include primality testing, factorization algorithms, probability and information theory, and collision resistance. This course offers a rigorous yet accessible path for students in mathematics and computer science to understand how abstract theory translates into the protection of information in a digital age.

Prerequisite: Linear Algebra preferred.
Credits: 4 credits
Textbook: An Introduction to Mathematical Cryptography, by Hoffstein, Pipher, and Silverman. ISBN-13: 978-1441926746

Syllabus

A first introduction to abstract algebra through ring theory and group theory, with an emphasis on concrete examples. The course will introduce basic notions (rings, subrings, groups, subgroups, homomorphisms, quotients) and prove some foundational results (Division algorithm, Lagrange’s theorem, Isomorphism theorems). Examples to be discussed include integers modulo n, matrix rings, polynomial rings, permutation groups, and dihedral groups.
Prerequisite: Linear Algebra.
Credits: 4 credits
Required text: Abstract Algebra, An Introduction (3rd ed.) by Hungerford; ISBN: 978-1111569624

Syllabus

This course is designed to give a firm grounding in the basic tools of analysis. It is recommended as preparation (but may not be a prerequisite) for other advanced analysis courses. Real and complex number systems, topology of metric spaces, limits, continuity, infinite sequences and series, differentiation, Riemann-Stieltjes integration.
Prerequisite: Linear Algebra and Calculus III.
Credits: 4 credits
Required text: Way of Analysis, Jones & Bart, ISBN: 9780763714970

Syllabus

This course continues AS.110.405 with an emphasis on the fundamental notions of modern analysis. Sequences and series of functions, Fourier series, equicontinuity and the Arzela-Ascoli theorem, the Stone-Weierstrass theorem, functions of several variables, the inverse and implicit function theorems, introduction to the Lebesgue integral.
Prerequisite: Real Analysis I
Credits: 4 credits
Required text: Way of Analysis, Jones & Bart, ISBN: 9780763714970

Syllabus

This is a continuation of Algebra I. Topics include: principal ideal domains, structure of finitely generated modules; introduction to field theory, linear algebra over a field, and Field extensions; splitting field of a polynomial, algebraic closure of a field; Galois theory: correspondence between subgroups and subfields. Solvability of polynomial equations by radicals.

Credits: 4 credits
Required Text: TBD

Syllabus

Topological spaces, connectedness, compactness, quotient spaces, metric spaces, function spaces. An introduction to algebraic topology including covering spaces, the fundamental group, and other topics are covered as time permits.

Credits: 4 credits
Required Text: Topology, 2nd Ed., Munkres, J., New Jersey: Prentice Hall, January, 2000, ISBN-10: 0131816292, ISBN-13: 978-0131816299

This course is the first in the sequence about the general theory of PDEs. The beginning of the course will describe several important results of functional analysis which are instrumental for the study of PDEs: Hahn-Banach theorem, Uniform boundedness and closed graph theorems, reflexive spaces and weak topologies. The topics covered include: theory of Sobolev spaces. Harmonic functions and their properties. Weyl theorem. General Elliptic operators. Existence theory for elliptic boundary value problems. Lax-Milgram theorem. Dirichlet principle. Fine properties of solutions of elliptic equations such as maximum principles, Harnack principles, Sobolev and Holder regularity.

Prerequisites: AS.110.201 Linear Algebra, AS.110.202 Calculus III, and AS.110.405 Real Analysis
Credits: 4 credits
Required Text: TBD

Syllabus

Algebraic geometry studies zeros of polynomials in several variables and is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometric problems about these sets of zeros. The fundamental objects of study are algebraic varieties which are the geometric manifestations of solutions of systems of polynomial equations. Algebraic geometry occupies a central place in modern mathematics and has multiple conceptual connections with diverse fields such as complex analysis, topology and number theory. This course aims to provide to an undergraduate student majoring in mathematics the fundamental background to approach the study of algebraic geometry by providing the needed abstract knowledge also complemented by several examples and applications.

Prerequisites: Linear Algebra and Abstract Algebra I

Credits: 3 credits
Required Text: Beginning in Algebraic Geometry, Clader & Ross. (https://link.springer.com/book/10.1007/978-3-031-88819-9)