The Mathematics Major

Mathematics students may choose to pursue a Bachelor of Science (BS) or a Bachelor of Arts (BA) degree in Mathematics. Click on a course title
to see a description of the course and information about it's offering in the Spring Semester 2012.
 Bachelor of Science Mathematics Major Requirements

The BS major in mathematics consists of the following courses:
• MATH 1170  Calculus Iplus two additional courses numbered above MATH 3000.
Goals: To learn how to use the calculus of one variable and the fundamental concepts of the calculus. Content: Limits, continuity, derivatives and integrals of functions of one variable. Applications are taken mostly from the physical sciences.
Goals: To learn how to use the calculus of one variable and the fundamental concepts of the calculus. Content: Integrals of functions of one variable, sequences and series. Applications are taken mostly from the physical sciences.
Goals: To extend concepts of calculus in two variables to the calculus of several variables. Content: Vector calculus, partial and total differentiation, maximum/minimum problems, multiple integration, line and surface integrals, vector and scalar fields, theorems of Green, Gauss, and Stokes.
Goals: To gain an appreciation for how abstract structures are used to solve theoretical and practical problems. Content: Systems of linear equations, matrices, determinants, vector spaces and bases, transformations, eigenvectors, introduction to linear differential equations.
Goals: To study mathematics as a logicodeductive system and to analyze those concepts and techniques that underlie all of mathematics. Content: Logic, proof construction, sets, relations, functions, mathematical induction, arguments involving infinite sets, number systems, axiomatics.
Goals: An introduction to algebraic structures includes groups and rings. Content: Equivalence relations. Peano Axioms. Fundamental Theorem of Arithmetic. Diophantine equations. The group of integers modulo n. Fundamental Theorem of Finite Cyclic Groups.
Goals: To begin the study of calculus from a mathematical point of view. In other words, to study the fundamental concepts of underlying the techniques of calculus. Content: Properties of complex numbers and analytic functions of one complex variable. Power series. Cauchy’s theorem, and applications to integration.
Goals: To continue the study of algebraic structures begun in MATH 3890 with the goal of seeing how the building of these mathematical models yields powerful tools to understand the global nature of mathematics. Content: Development of the elementary concepts of groups, rings, and fields.
Goals: To continue the stydy of the structure of differentiable and integrable functions begun in Math 3910. Content: An introduction to real analysis with emphasis on proofs of theorems and on problem solving. Topics include properties of the real number system, functions, sequences, limits and continuity, differentiation, integration, and infinite series including sequences and series of functions.
Goals: The student will be introduced to ideas and issues that are outside of the regular undergraduate curriculum, studying how mathematics is used in academia and industry. Content: Reviews of current research and projects of various mathematicians: senior math majors, guest lecturers, and department staff. Student presentations of topics from internships, independent studies, or honors projects.
Goals: The student will be introduced to ideas and issues that are outside of the regular undergraduate curriculum, studying how mathematics is used in academia and industry. Content: Reviews of current research and projects of various mathematicians: senior math majors, guest lecturers, and department staff. Student presentations of topics from internships, independent studies, or honors projects. Goals: To synthesize previous work in the various areas of mathematics with the goal of putting the areas in a historical perspective and of relating them to the question of what makes up mathematics. Content: The content of the seminar varies from year to year depending on the instructor. Attention is paid to the history of mathematics and to filling gaps in the spectrum of mathematics presented at the undergraduate level.  Bachelor of Arts Mathematics Major Requirements

The BA major in mathematics consists of the following courses:
• MATH 1170  Calculus Iplus two additional courses numbered above MATH 3000.
Goals: To learn how to use the calculus of one variable and the fundamental concepts of the calculus. Content: Limits, continuity, derivatives and integrals of functions of one variable. Applications are taken mostly from the physical sciences.
Goals: To learn how to use the calculus of one variable and the fundamental concepts of the calculus. Content: Integrals of functions of one variable, sequences and series. Applications are taken mostly from the physical sciences.
Goals: To gain an understanding of applied statistics with emphasis on multivariate statistical analysis building on the concepts learned in elementary statistics courses. Content: Topics will include statistical models motivated by examples drawn from diverse fields including economics, education, and biology; model selection and factor analysis; maximum likelihood; multiple regression; MANOVA; logistic regression; and the bootstrap.
Goals: To extend concepts of calculus in two variables to the calculus of several variables. Content: Vector calculus, partial and total differentiation, maximum/minimum problems, multiple integration, line and surface integrals, vector and scalar fields, theorems of Green, Gauss, and Stokes.
Goals: To gain an appreciation for how abstract structures are used to solve theoretical and practical problems. Content: Systems of linear equations, matrices, determinants, vector spaces and bases, transformations, eigenvectors, introduction to linear differential equations.
Goals: To study mathematics as a logicodeductive system and to analyze those concepts and techniques that underlie all of mathematics. Content: Logic, proof construction, sets, relations, functions, mathematical induction, arguments involving infinite sets, number systems, axiomatics.
Goals: An introduction to algebraic structures includes groups and rings. Content: Equivalence relations. Peano Axioms. Fundamental Theorem of Arithmetic. Diophantine equations. The group of integers modulo n. Fundamental Theorem of Finite Cyclic Groups.
Goals: To begin the study of calculus from a mathematical point of view. In other words, to study the fundamental concepts of underlying the techniques of calculus. Content: Properties of complex numbers and analytic functions of one complex variable. Power series. Cauchy’s theorem, and applications to integration.
Goals: The student will be introduced to ideas and issues that are outside of the regular undergraduate curriculum, studying how mathematics is used in academia and industry. Content: Reviews of current research and projects of various mathematicians: senior math majors, guest lecturers, and department staff. Student presentations of topics from internships, independent studies, or honors projects.
Goals: The student will be introduced to ideas and issues that are outside of the regular undergraduate curriculum, studying how mathematics is used in academia and industry. Content: Reviews of current research and projects of various mathematicians: senior math majors, guest lecturers, and department staff. Student presentations of topics from internships, independent studies, or honors projects. Goals: To synthesize previous work in the various areas of mathematics with the goal of putting the areas in a historical perspective and of relating them to the question of what makes up mathematics. Content: The content of the seminar varies from year to year depending on the instructor. Attention is paid to the history of mathematics and to filling gaps in the spectrum of mathematics presented at the undergraduate level.
The Mathematics Minor
The minor in mathematics consists of the following courses:
• MATH 1170  Calculus I
• MATH 1180  Calculus II
• MATH 5920  Junior Seminar (fall and spring term)
• MATH 5930  Senior Seminar (fall and spring term)
plus four additional courses numbered above MATH 1180 with two chosen from the following:
Goals:  To learn how to use the calculus of one variable and the fundamental concepts of the calculus.  
Content:  Limits, continuity, derivatives and integrals of functions of one variable. Applications are taken mostly from the physical sciences. 
Goals:  To learn how to use the calculus of one variable and the fundamental concepts of the calculus.  
Content:  Integrals of functions of one variable, sequences and series. Applications are taken mostly from the physical sciences. 
Goals:  To extend concepts of calculus in two variables to the calculus of several variables.  
Content: 
Goals:  The student will be introduced to ideas and issues that are outside of the regular undergraduate curriculum, studying how mathematics is used in academia and industry.  
Content: 
• MATH 3330  Linear Algebra
• MATH 3440  Discrete Mathematics
• MATH 3550  Foundations of Mathematics
• MATH 3560  Modern Geometry
• MATH 3720  Differential Equations
• MATH 5810  Probability and Mathematical Statistics
• MATH 5890  Algebra II
• MATH 5910  Analysis II
Goals:  To gain an appreciation for how abstract structures are used to solve theoretical and practical problems.  
Content: 
Goals:  To introduce the concept of the discrete as well as techniques used in higher noncontinuous mathematics, providing the necessary background material required by computer scientists for algorithm analysis.  
Content:  Sets and numeration, combinatorics, logic, algorithms, recursion, generating functions, graphs, and trees. 
Goals:  To study mathematics as a logicodeductive system and to analyze those concepts and techniques that underlie all of mathematics.  
Content:  Logic, proof construction, sets, relations, functions, mathematical induction, arguments involving infinite sets, number systems, axiomatics. 
Goals:  To introduce to the concept of model building in mathematics from both a synthetic and an axiomatic point of view.  
Content:  Various geometries are studied with attention paid to what geometry is. Hilbert’s axiom system for Euclidean geometry, hyperbolic geometry, and transformations. 
Goals:  To introduce techniques and methods of mathematics especially appropriate to the physical sciences.  
Content:  Introductory ordinary differential equations, linear partial differential equations, emphasizing separation of variables, Fourier series, special functions. 
Goals:  To gain an understanding of both probability and statistics as not merely collecting and organizing data but as the science of basing inferences on observed data and making decisions in the face of uncertainty. The student will be prepared to take the preliminary actuarial examination in probability and statistics.  
Content:  Probability distributions, mathematical expectation, random variables, point and interval estimation, hypothesis testing, regression and correlation, analysis of variance. 
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