• 100's
    • [MACS-101] Introduction to Actuarial Science The course consists of presentations introducing various topics dealt with by actuaries, weekly lab activities to provide in-depth work with these ideas, and presentations from actuaries regarding their work. Specific topics include mortality tables, interest theory, probability, principles of insurance and reserves.
    • [MATH-105] Fundamentals of Mathematics Integers, rational numbers, exponents, order of operations. Functions in context, and their algebraic and graphical representation. Linear and quadratic equations. Introduction to the graphing calculator.
    • [MATH-110] Intro to Quantitative Reasoning This course creates a foundation for students to develop their Numeracy skills and confidence when dealing with quantitative information in every-day life. These quantitative skills have become necessary for anyone who wants to lead a well-informed and impactful life in today's data-entrenched world and society. We will read many magazine and newspaper articles and book excerpts, we will learn to use Excel to produce graphs, and to help us with otherwise complicated calculations about loans and savings, we will learn to distinguish between 'Size' and 'Relative Size' and to use appropriate language to express each. Ideas like percentages, rates, ratios, and proportionality will be a major focus. This course does not require a strong mathematical background, and is therefore an alternative mathematics entry point for many students.
    • [MATH-113] Mathematics of Finance Simple and compound interest, discounting, annuities, amortization and sinking funds, stocks, bonds, insurance.
    • [MATH-115] Topics in Applied Mathematics Topics in the application of elementary mathematics to real world problems: management science, voting schemes, theory of games, population growth, other models.
    • [MATH-116] Elementary Statistics An introduction to statistical thinking and its applications to a wide variety of areas. Topics include: statistical and visual methods for summarizing data, basic principles of probability, regression, and fundamentals of hypothesis testing and confidence intervals. Critical examination of the results of a statistical analysis is emphasized.
    • [MATH-120] Elementary Functions Graphs and properties of functions, including polynomial functions, exponential functions, logarithmic functions, inverse functions and composition of functions. Applications to real world situations using algebraic, numerical, and graphical methods.
    • [MATH-125] Explorations in Mathematics Exploration of easily accessible, engaging, and thematically connected mathematical ideas as a vehicle to lead students to experiences that are characteristic of the mathematical enterprise. Individual Course Descriptions
    • [MATH-140] Concepts of Calculus An informal introduction to a study of quantities that change relative to each other and the fundamental concepts of the calculus which measure this change: the derivative and the integral.
    • [MATH-147] Calculus from an Historical Perspective An overview of concepts from differential and integral calculus through excerpted readings in English translation of original texts which emphasizes connections with developments in science and philosophy.
    • [MATH-150] Elements of Calculus I Modeling data with polynomial functions, exponential functions, and logistic functions. Rates of change and the derivative. Application of the derivative including optimization and inflection points. Result of cumulative change and the definite integral.
    • [MATH-151] Elements of Calculus II Modeling with trigonometric functions, functions of several variables, contour maps, partial derivatives, and optimization with and without constraints.
    • [MATH-154] Milestones in Mathematics Charts milestones in various branches of mathematics through the reading of original sources: number theory, infinity, Euclidean and non-Euclidean geometry, and algebra are all possible threads of development.
    • [MATH-156] General Statistics An introduction to the major concepts and tools used for collecting, analyzing, and making inferences from data. Topics include: graphical displays, correlation, regression, design of experiments, probability, simulation, random sampling, confidence intervals and hypothesis testing.
    • [MATH-158] General Statistics II A second course in statistics covering various methods of data analysis. Topics include: t-tests, analysis of categorical data, estimation and inference of multiple regression models, Analysis of Variance, and multiple comparisons. The ability to communicate and correctly interpret the results of a statistical data analysis is emphasized.
    • [MATH-169] Precalculus This is a study of linear, polynomial, rational, exponential, logarithmic, and trigonometric functions from symbolic, graphical, and numerical perspectives. Topics include algebraic and analytic properties of functions; sums, differences, products, quotients, and composites of functions; inverse functions; and functions as models.
    • [CSCI-170] Computer Science I
    • [MATH-170] Calculus I Limits and continuity. Transcendental functions. The derivative, techniques of differentiation, and applications of the derivative. Parametric equations. The definite integral, numerical integration, antiderivatives, and method of substitution.
    • [MATH-171] Calculus II Numerical integration, applications of the definite integral, techniques of integration, and improper integrals. Taylor polynomials. Sequences and series. Polar coordinates.
    • [MATH-191] Orientation to the Major The objective of the course is to to familiarize students with the mathematics major and possible careers in the field. You will learn what distinguishes pure mathematics, applied mathematics, statistics, mathematics education and actuarial science as well as what the fields have in common. You will receive exposure to possible careers in mathematics after graduation and opportunities to gain additional experience during your time at Xavier (REU's, internships, etc.). You will gain technical skills that will aid in your development as a mathematician (e.g. how to typeset in LATEX, how to give a mathematics talk, how to use computational software).
  • 200's
    • [MACS-201] Actuarial Mathematics An introduction to Actuarial Mathematics. Topics include survival distributions and life tables, force of morality, laws of morality, life insurance, life annuities, benefit premiums, and benefit reserves.
    • [MATH-201 ECED] Foundations of Arithmetic Concepts necessary for understanding the structure of arithmetic and its algorithms (with whole numbers, integers, fractions and decimals), number patterns, and introductory probability and statistics.
    • [MATH-202 ECED] Geometry and Measurement Concepts necessary for an understanding of basic geometry: shapes in one, two, and three dimensions, scientific measurement and dimensional analysis, congruence and similarity of figures, compass and straightedge constructions, transformations, and coordinate geometry. Use of computer software to explore geometric concepts.
    • [MATH-211 MCED] Foundations of Arithmetic Concepts necessary for understanding the structure of arithmetic, its algorithms and properties (with whole numbers, integers, rational and irrational numbers), basic set theory and introductory number theory.
    • [MATH-212 MCED] Geometry and Measurement Concepts necessary for an understanding of basic geometry: shapes in one, two, and three dimensions, scientific measurement and dimensional analysis, congruence and similarity of figures, compass and straightedge constructions, transformations, coordinate geometry, conjecture and proof, perspective drawing and introductory trigonometry. Use of computer software to explore geometric concepts.
    • [MATH-213 MCED] Algebra Concepts Development of algebraic problem solving, polynomials, linear, quadratic and exponential equations and functions, pattern representation, sequences and series. Use of technology and manipulative materials in the teaching of algebra.
    • [MATH-214 MCED] Mathematical Problem Solving Problem solving, drawing from a wide range of school mathematics topics, logic, combinatorics, and basic probability theory.
    • [MATH-220] Calculus III Vectors, lines and planes. Functions of several variables, partial derivatives and applications, gradient and directional derivative. Multiple integrals, line integrals, Green’s Theorem.
    • [MATH-222] Applied Linear Algebra An introduction to elementary linear algebra with an emphasis on application and interpretation. Topics include systems of linear equations and their solutions, matrix algebra, linear transformations, determinants, inverses, eigenvalues and eigenvectors, orthogonality. Selected applications to physical and social sciences.
    • [MATH-225] Foundations of Higher Mathematics Propositional and predicate logic; methods of proof, including direct approaches, contradiction, contraposition, mathematical induction; sequences, recursion, recurrence relations; set theory; functions and relations. Primary emphasis on proof-writing.
    • [MATH-230] Introduction to Ordinary Differential Equations Modeling with ordinary differential equations. Analytical, qualitative, and numerical techniques for first-order equations, first-order nonlinear systems, and linear systems.
    • [MATH-240] Linear Algebra Systems of linear equations, Gaussian elimination, echelon forms, algebraic structure of solutions; vector and matrix arithmetic, invertibility; linear transformations and their matrices; vector spaces and subspaces, bases, coordinates, dimension, rank; change of basis; determinants, Cramer’s Rule; eigenvectors and eigenvalues; diagonalization; inner products, the Gram-Schmidt process.
    • [MATH-256] Introduction to Probability and Statistics Calculus-based introduction to probability and descriptive and inferential statistics. Topics include: numerical and graphical summaries of data, conditional probability, Bernoulli trials, normal distribution, the central limit theorem, estimation, t-tests, chi-square tests, type I and II errors, regression and correlation.
    • [MATH-257] Data Modeling Exploratory data analysis and visualization, logistic regression, estimation and inference of multiple regression models, model selection, Analysis of Variance, multiple comparisons, and experimental design.
    • [MATH-280] Combinatorics An introduction to counting techniques of discrete objects. The enumeration of sets, permutations and combinations, the binomial and multinomial theorem will serve as an appetizer; counting methods including the inclusion-exclusion principle; the pigeonhole principle, generating functions, and recurrence relations will be the main course. Applications of combinatorial techniques and problem solving will be emphasized. [Optional: finite geometries, permutation groups, latin squares, designs, and codes.]
    • [MATH-291] Introduction to Maple An introduction to Maple, a general purpose symbolic computing environment for the analysis, exploration, visualization, and solution of a wide range of mathematical problems.
    • [MATH-295] Introduction to LaTeX An introduction to the mathematical typesetting markup language LaTeX.
    • [MATH-296] Introduction to R An introduction to R, an open-source statistical programming language, and the R Studio interface.
  • 300's
    • [MATH-300] History of Mathematics Some of the highlights in the historical development of mathematics with special attention given to the invention of non-Euclidean geometry and its importance for mathematics and Western thought.
    • [MATH-301] Geometry Axiom systems, models and finite geometries, convexity, transformations, Euclidean constructions, and the geometry of triangles and circles. Introduction to projective and non-Euclidean geometries.
    • [MATH-302] Number Theory Divisibility and primes, linear congruences, quadratic residues and reciprocity. Diophantine equations, multiplicative functions, distribution of primes.
    • [MATH-303] Mathematical Logic Axiomatic development of propositional calculus, functional complete sets of operators, axiomatic development of the first order function calculus, the existential operator, the algebra of logic.
    • [MATH-311] Probability Theory Sample spaces, basic axioms of probability, Bayes’ theorem, expectation, common discrete and continuous distributions, moment generating functions, central limit theorem, inequalities, convergence of random variables, and transformations of random variables.
    • [MATH-312] Statistical Inference Maximum likelihood principle, Bayesian estimation, properties of estimators, sufficiency, likelihood ratio tests, chi-square distribution, t distribution, F distribution, power, nonparametrics, bootstrap, and Markov Chain Monte Carlo.
    • [MATH-316] Cryptology The making and breaking of secret ciphers and codes. Classical ciphers: shift, affine, Vigenère, substitution, Hill, one-time pads, and Enigma. A brief introduction to number theory. Modern methods: RSA algorithm, DES, AES: Rijndael, discrete logarithms and elliptic curves.
    • [MATH-321] Numerical Analysis Accuracy, function evaluation and approximation, systems of linear equations, nonlinear equations, numerical differentiation and integration, and solutions to differential equations.
    • [MATH-325] Mathematical Modeling The synthesis, formulation and solution of various problems in applied mathematics and related fields.
    • [MATH-330] Graph Theory Graphs, subgraphs, trees, isomorphism, Eulerian and Hamiltonian paths, planarity, digraphs, connectivity, and chromatic number. Other topics may be included.
    • [MATH-340] Abstract Algebra I Groups, isomorphism, homomorphism, normal subgroups, rings, ideals, fields.
    • [MATH-341] Abstract Algebra II A continuation of MATH 340. Topics may include Boolean algebra, lattice theory, combinational group theory, coding theory, Galois theory, commutative rings.
    • [MATH-360] Elementary Topology Metric spaces, topological spaces, continuity, convergence, compactness, connectedness, and separation axioms.
    • [MATH-370] Real Analysis Rigorous development of calculus of functions of a single variable. The real number system, topology of the real line, continuity, uniform continuity, the derivative, the Riemann integral, sequences and series of real numbers, and uniform convergence.
    • [MATH-372] Applied Analysis Special functions, orthogonal sets of functions. Sturm-Liouville theory. Partial Differential Equations. Fourier series, integrals and transforms.
    • [MATH-380] Introduction to Complex Variables Complex numbers, analytic functions, complex integration, series representation of analytic functions, the calculus of residues.
    • [MATH-385] Secondary Mathematics from an Advanced Perspective A capstone course for prospective high school teachers focusing on connections between secondary and undergraduate mathematics. Emphasis on analysis and algebra. The real numbers, sequences and series, countability, concepts of infinity. Functions, logarithms, solving equations, the Fundamental Theorem of Algebra and its consequences. Complex numbers and functions.
    • [MATH-391] Mathematics Seminar 1 Juniors (MATH 391) and seniors (MATH 393) meet together in the spring semester.  Students will read selections from the mathematical literature, explore how to write mathematics effectively, learn how to use technical word processing tools, practice how to communicate mathematical ideas and give oral presentations.
    • [MATH-392] Mathematics Seminar 2 Each senior will meet with a faculty advisor to work on an individual research project.
    • [MATH-393] Mathematics Seminar 3 The student will write a paper and give a formal presentation describing the project developed during MATH 392.
    • [MATH-397] Special Study Credit by special arrangement. Area to be specified.
  • 500's
    • [MATH-516] Introduction to Statistics A graduate-level introduction to statistical thinking and its applications to a wide variety of areas. Topics include: statistical and visual methods for summarizing data, basic principles of probability, regression, and fundamentals of hypothesis testing and confidence intervals. Critical examinations of the results of a statistical analysis in SAS are emphasized.