This course covers the fundamentals of algebra, ranging from linear equations and their graphs through exponents and systems of equations.

This course investigates mathematical modeling applied to a variety of topics such as linear programming, coding information, probability and statistics, scheduling problems and social choice.

This course covers algebraic topics ranging from functions and their applications to complex numbers to inverse functions to the fundamental theorem of algebra.

This course covers topics ranging from exponential and logarithmic functions to trigonometric functions to the complex plane and elementary optimization problems.

An introduction to calculus focused on business applications. The following topics are considered: modeling change using algebraic, exponential and logarithmic functions, derivatives, optimization, integration, functions of two variables, and partial derivatives.

An introduction to differential and integral calculus, with an emphasis on applications. This course is intended for students in the life and social sciences, computer science, and business. Topics include: modeling change using functions including exponential and trigonometric functions, the concept of the derivative, computing the derivative, applications of the derivative to business and life, social and computer sciences, and an introduction to integration.

This course is a continuation of MATH 131. Topics include: definition and interpretations of the integral (numerically, graphically, and algebraically), basic techniques for computing anti-derivatives, applications to probability, an introduction to multi-variable calculus and optimization for functions of several variables, and mathematical modeling using differential equations. (This course is not a substitute for MATH 162.)

The content covered in this course will include: Area, perimeter, volume, surface area, Properties of two and three dimensional figures, points, lines, planes, space, the Pythagorean theorem, transformations, fractals, tessellations, perspective drawings and informal proofs. The material covered will address Illinois Learning Standard Goal 7 and Goal 9 and related content performance descriptors for educators. The course is designed for Elementary education majors that wish to enhance, enrich and deepen their knowledge of Geometry and apply for a 6th-8th grade Mathematics endorsement from the State of Illinois. Mathematics Content Area Standards 7 (Measurement) and 9 (Geometry) from the Content-Area Standards for Educators document published by the Illinois State Board of Education will be emphasized.

Greatest common divisors, prime factorization, decimal fractions, continued fractions, primes, composite numbers, tests for divisibility, perfect numbers, polygonal numbers, numbers bases, and patterns in addition and multiplication tables are a sample of the topics covered. (Illinois Learning Standard Goal 6 and related performance descriptors). Appropriate use of technology (spread sheets, CAS, etc.) will also be addressed.

This course will provide a thematic approach to the history of mathematics with emphasis on contributions by noted mathematicians, mathematical societies and scientists highlighting women and under-represented populations. The history of numbers and numerals, computation, geometry, algebra, trigonometry, calculus, and science patterns will be explored emphasizing the contributions of the Babylonian, Egyptian, Chinese, and Roman civilizations as well as such individuals as Euclid, Fermat, Archimedes, Kepler, Pythagoras, Euler, Hypatia, Sonjs Kovalevsky, Emmy Noether and others as appropriate. The influence of technology and its applications will also be presented as appropriate.

Data collection and display, simulations, surveys, probability and elementary statistics such as mean, median, mode, standard deviation, etc. will be the focus of this course (Illinois Learning Standard Goal 10) Appropriate techniques for graphing (scatter plots, histograms, regression, correlation) with and without technology will be a focus of this course.

This course provides a standard introduction to differential and integral calculus and covers topics ranging from functions and limits to derivatives and their applications to definite and indefinite integrals and the fundamental theorem of calculus and their applications.

This course is a continuation of Calculus I and includes the calculus of various classes of functions, techniques of integration, applications of integral calculus, three-dimensional geometry, and differentiation and integration in two variables.

This course is a continuation of Calculus I and includes the calculus of various classes of functions, techniques of integration, applications of integral calculus, sequences and infinite series, and an introduction to differential equations. This course follows a traditional approach to calculus sequencing.

Students will learn best practices to communicate mathematical concepts and skills to diverse populations by engaging in tutoring mathematics to the undergraduate population at Loyola. This course is designed to promote and encourage engagement and rigor in mathematical concepts and skills among the diverse communities of learners at Loyola.

This course covers topics from discrete mathematics and number theory, areas of mathematics not seen in calculus courses and abundant in applications, that provide students with the concepts and techniques of mathematical proof needed in 300 level courses in mathematics.

This course provides an introduction to linear algebra in abstract vector spaces with an emphasis on Rn, covering topics such as Gaussian elimination, matrix algebra, linear independence and spanning, linear transformations and eigenvalues; software packages such as MAPLE may be used.

This is an introductory programming course for students interested in mathematics and scientific computing. Students will program primarily in a general object-oriented language such as Python, with supplementary exercises in a computer algebra system. Examples will be drawn primarily from applications of calculus, elementary number theory, and cryptography.

This course covers the differential and integral calculus of multivariable and vector valued functions, and sequences and infinite series, culminating with Green's Theorem, the Divergence Theorem, and Stokes' Theorem; software packages such as MAPLE may be used.

This course covers the differential and integral calculus of multivariable and vector valued functions, culminating with Green's Theorem, the Divergence Theorem, and Stokes' Theorem; software packages such as MAPLE may be used. This course follows a traditional approach to calculus sequencing.

This course covers the theory, solution techniques, and applications surrounding linear and non-linear first and second-order differential equations, including systems of equations; software packages such as MAPLE may be used.

This course provides an introduction to basic topics in ordinary differential equations and linear algebra. Topics include first and second-order differential equations, Laplace transform, systems of first-order differential equations, systems of linear algebraic equations, matrix algebra, bases and dimension for vector spaces, linear independence, linear transformations, determinants, eigenvalues, and eigenvectors. Prerequisites or

This course is a sophomore-level seminar covering topics in areas such as number theory, logic, set theory, metric spaces, or history of mathematics.

This course explores selected topics in the history of mathematics ranging from Babylonian and Egyptian mathematics to Pythagoras and Euclid to the Hindu-Arabic numeration system to Newton and Leibniz to geometries other that Euclid's to the mathematical art of Escher.

This course offers an introduction to topics such as error analysis, interpolation and approximation, and the numerical solution of problems involving differentiation, integration, and ordinary and partial differential equations.

This course provides a rigorous introduction to the study of structures such as groups, rings, and fields; emphasis is on the theory of groups with topics such as subgroups, cyclic groups, Abelian groups, permutation groups, homomorphisms, cosets, and factor groups.

This course studies advanced algebraic systems such as commutative and non-commutative rings, integral domains, fields, and additional selected topics.

This course offers a rigorous abstract approach to vector spaces and transformations, including similarity, duality, canonical forms, inner products, bilinear forms, Hermitian and unitary spaces, and other selected topics.

This course offers a rigorous introduction to combinatorics, including topics such as induction, the pigeon-hole principle, permutations, combinations, recurrence relations, generating functions, the inclusion-exclusion principle, and other selected topics.

This course in modern mathematical logic begins with a study of propositional logic and leads to the study of first-order predicate logic, including quantifiers, models, syntax, semantics, the completeness and compactness theorems, and other selected topics.

This course will cover Pythagorean triples, problems related to Fermat's Last Theorem, Pell's equation, Fermat's method of descent, primes in arithmetic progressions, Mersenne primes, perfect numbers, primitive roots, primality testing, Carmichael numbers, RSA public key encryption, quadratic residues, and quadratic reciprocity. Additional topics will be covered as time permits.

This course introduces the formal foundations of cryptography and also investigates some well-known standards and protocols, including private and public key cryptosystems, hashing, digital signatures, RSA, DSS, PGP, and related topics.

This course discusses axiomatic systems which define geometries and includes topics from synthetic and analytic projective geometry.

The course provides an introduction to the mathematical theory of option pricing. We will rigorously derive option relationships using no arbitrage conditions, introduce rudimentary stochastic calculus and Brownian motion as models for stock prices, and give an introduction to methods for solving partial differential equations to give explicit Black-Scholes formulas.

This course provides a rigorous treatment of the real numbers and real-valued functions of a real variable, including sequences, the Bolzano-Weierstrass and Heine-Borel theorems, topology, uniform continuity, fixed-point theorems, derivatives, and other selected topics.

This course, a continuation of MATH 351, provides the theoretical background for differentiability and integrability on R and Rn and Taylor's theorem, the change of variable theorem, the inverse and implicit function theorems, Lebesgue integration, and other selected topics.

This course provides an introduction to the theory of functions of a complex variable, including analytic functions, contour integrals, the Cauchy integral formula, harmonic functions, Laurent series, residues and poles, conformal mapping, and other selected topics.

Vector calculus, linear transformations, matrices, series solutions of differential equations, special functions; Fourier series, Fourier and Laplace transforms; Partial differential equations and topics from complex analysis, Green's functions, integral equations, the calculus of variations.

This course will teach students how to use various areas of mathematics, such as vector calculus, linear algebra, and ordinary differential equations, to formulate mathematical models in, for example, particle and continuum mechanics, biology, economics, finance, etc.

The course is an introduction to linear, nonlinear, and integer optimization, and may include optimization on graphs, stochastic optimization, etc. Modeling of real-life problems as optimization problems, mathematical analysis of resulting optimization problems, and computational approaches to solving the problems will be covered.

This course provides an introduction to basic topics in partial differential equations (PDE). In addition to first order PDE, such as the transport equation, the main types of second order PDE, including the Laplace equation, the heat equation, and the wave equation, will be studied in detail.

This course introduces formal language theory, including such topics as finite automata and regular expressions, pushdown automata and context-free grammars, Turing machines, undecidability, and the halting problem.

This first course in topology discussed topological spaces, continuity, connectedness, path-connectedness, compactness, product spaces, quotient spaces, Tychonoff's theorem, the Baire category theorem, and other selected topics.

This course covers advanced topics in mathematics, including analysis, topology, algebra, applied mathematics, and logic.

The seminar will cultivate students' presentation skills through participation in and critical discussion of brief lectures on familiar and unfamiliar topics; preparation and presentation of two brief lectures by the student (one on a familiar topic from the curriculum, one on a higher level material not customarily from the curriculum); and preparation of an extended abstract summarizing the advanced material presented.

The course unifies the knowledge gained in previous Mathematics courses and provides an opportunity for in-depth study and presentation of advanced material not usually covered in the standard Mathematics curriculum.

This course allows students to engage in independent study on selected topics in mathematics under the supervision of a faculty member.

This is a professional development seminar for the beginning graduate student. Through short lectures, faculty panels, career panels, regular reading and writing assignments, and assorted workshops, it provides the student with the tools they need to succeed in the program, and beyond.

A survey course in three parts. I: the theorems of Burnside, Sylow, and Jordan-Holder, toward the classification of finite simple groups. II: (noncommutative) rings and modules over PIDs, including applications to classification problems. III: additional topic chosen by instructor, e.g., category theory, homological algebra, division rings, and representation theory.

This course will be a mathematical study of the concepts of truth and proof and how they relate to each other. The main topics to be covered are propositional logic, first order predicate logic, computability and undecidability results.

Topics chosen from: Pythagorean triples, Fermat's Last Theorem, Pell's equation, Fermat descent, primes in arithmetic progressions, Mersenne primes, perfect numbers, primitive roots, primality testing, Carmichael numbers, RSA encryption, quadratic residues, quadratic reciprocity, integers as the sum of squares, Gaussian integers, continued fractions, the distribution of primes, Diophantine approximation, elliptic curves; others.

An introduction to functions of a single complex variable. Topics include analytic functions, contour integrals, Cauchy integral formula, harmonic functions, Liouville's theorem, Laurent series, analytic continuation, and conformal mapping. Additional topics may include theorems of Picard and Rouché, the Riemann mapping theorem, Riemann surfaces, and the fast Fourier transform.

An introduction to advanced topics in analysis, including measure theory, functional analysis and partial differentials equations. Measurable sets; the Lebesgue integral in Rn; Lp and other function spaces; weak convergence; Lax-Milgram Theorem; and the calculus of variations. These topics are then applied to the study of linear PDEs. Students will be able to apply these concepts to study PDEs.

This course will provide a thematic approach to the history of mathematics with emphasis on contributions by noted mathematicians, mathematical societies and scientists highlighting women and under-represented populations. The history of numbers and numerals, computation, geometry, algebra, trigonometry, calculus, and science patterns will be explored emphasizing the contributions of the Babylonian, Egyptian, Chinese, and Roman civilizations as well as such individuals as Euclid, Fermat, Archimedes, Kepler, Pythagoras, Euler, Hypatia, Sonja Kovalevsky, Emmy Noether and others as appropriate. The influence of technology and its applications will also be presented as appropriate.

Data collection and display, simulations, surveys, probability and elementary statistics such as mean, median, mode, standard deviation, etc. will be the focus of this course (Illinois Learning Standard Goal 10) Appropriate techniques for graphing (scatter plots, histograms, regression, correlation) with and without technology will be a focus of this course.

Mathematical concepts such as rates, ratios and proportions, probability and statistics and measurement that support scientific investigation and analysis will provide the focus for this course. Hands-on activities that illustrate the connections be used. Hands-on activities that illustrate the connections between Science and Math and appropriate use of technology will be emphasized.

A project-based course. Under faculty consultation, students will design and independently carry out a research project devoted to the development, pedagogy, or application of mathematics. To earn credit for this course, the student will deliver both an oral presentation and technical paper at the level expected in the professional workplace.