Mathematics

Mathematics students at Hanover learn to reason through problems to find a solution, express ideas clearly and recognize relations among seemingly dissimilar situations. As a mathematics or computer science major, you will become a creative thinker who can analyze a wide range of situations. You will master the skill of simplifying the complex. With small class sizes and a dedicated faculty, Hanover also lets you follow your particular interests through internships and independent study programs.

### What do mathematics majors study?

- Calculus
- Logic, sets and relations
- Linear algebra
- Algebraic systems
- Probability and statistics
- Other topics that interest you, from the foundations of geometry to topology

### Mathematics placements

Previous graduates' career and professional placements have included:

- Actuarial Analyst, CNA Insurance
- Financial Analyst, Eli Lilly & Co (Indianapolis)
- Programmer, Nims Associates
- Math Teacher, Farrington High School (Hawaii)
- Systems Analyst, Fifth Third Bank
- Actuary, AON
- Technical Analyst, Sim2k

Graduate school placements have included:

- Carnegie Mellon University
- Purdue University
- University of Illinois
- Whittier Law School
- University of Iowa
- University of Cincinnati
- University of Kentucky
- Indiana University

### Courses

Number

Name

Units

Description

MAT 113

Essential Precalculus

1

A review of the precalculus topics which are essential for success in Calculus: inequalities; equations and their graphs; functions (polynomial, rational, trigonometric, exponential, and logarithmic). Includes an introduction to the concepts of limit, tangent line slope, and area beneath a curve. Does not count toward a major or minor in Mathematics.

MAT 121

Calculus I

1

An introduction to the theory of differential and integral calculus for functions of one variable. Includes the concepts of limit, continuity, derivatives, and indefinite integrals and definite integrals, culminating in the Fundamental Theorem of Calculus. Applications to related rates and optimization problems. Recommended: A strong background in algebra and trigonometry, or 113. Students are advised to take the departmental placement exam to assess their proficiency in algebra and trigonometry. Partially satisfies the SM CCR and satisfies the QL ACE.

MAT 122

Calculus II

1

Differentiation and integration of logarithmic functions, exponential functions, and inverse trigonometric functions. Study of polar coordinates, conic sections, and various integration techniques. Applications to computations of volumes, surface areas, and centers of mass. Prerequisite: 121 or equivalent college course, or placement via departmental placement test. Partially satisfies the SM CCR and satisfies the QL ACE.

MAT 210

Math Topics for Liberal Arts

1

Non-technical introduction to selected concepts of modern mathematics (such as logic, set theory, axiomatic systems, non-Euclidean geometry, number theory, graph theory, etc.) that illustrate the nature of mathematics and its connections to other areas of knowledge. Does not count toward major or minor. Partially satisfies the SM CCR and satisfies the QL ACE.

MAT 212

Mathematics for Elementary Teachers

1

A study of mathematical concepts that are taught in elementary school, including problem solving, sets, numbers and their properties, operations on sets and numbers, geometry, measurements, probability and statistics. Does not count toward a major or minor in math. Prerequisite: EDU 221. Partially satisfies the SM CCR.

MAT 217

Applied Statistics

1

Use of graphs and numerical summaries to describe data from individual variables and to investigate relationships among variables. Design of statistical experiments. Survey of fundamental concepts of probability, including sampling distributions. Use of sample data to estimate, and to test hypotheses about, unknown parameters. Does not count toward major. No prerequisites. Partially satisfies the SM CCR and satisfies the QL ACE.

MAT 220

Logic, Sets and Relations

1

An introduction to the foundations of mathematics, with emphasis on developing basic reasoning skills needed for constructing proofs. Required for major. Counts toward minor but not in addition to Mat 243. Partially satisfies the SM CCR.

MAT 221

Calculus III

1

Differentiation and integration of vector-valued functions. Study of functions of several variables, including partial derivatives and multiple integrals. Detailed study of infinite sequences and series. Prerequisite: 122 or equivalent. Satisfies the Abstraction and Formal Reasoning LADR.

MAT 224

Linear Algebra

1

Systems of linear equations and their solutions. Study of the algebraic properties and applications of vectors, matrices, and linear transformations. Prerequisite: 121.

MAT 231

Differential Equations

1

Survey of basic techniques for describing dynamical systems by means of equations involving derivatives of functions, and of methods for finding functions which satisfy these equations. Prerequisite: 122.

MAT 243

Discrete Mathematics I

1

A survey of the math topics which are foundational to computer science: functions, relations, sets, basic logic, proof techniques, combinatorics, graphs and trees, discrete probability. No prerequisite. Partially satisfies the SM CCR.

MAT 311

History of Mathematics

1

Survey of important discoveries in mathematics and the historical contexts in which they were made. Topics will include major mathematical developments beginning with the Ancient Greeks and tracing the development through Hindu, Arabic and European mathematics up to the modern developments of the 20th century. Prerequisite: 121 or permission.

MAT 320

Introduction to Number Theory

1

Explores properties of the integers such as divisibility and congruence, linear diophantine equations, prime numbers, the Fundamental Theorem of Arithmetic, Fermat's little theorem, Euler's Theorem, Euler's phi function, computing powers and roots in modular arithmetic, and public key cryptography. Prerequisite: Mat 243 or 220.

MAT 321

Introduction to Real Analysis

1

Development of the algebraic and topological properties of the real number system and the theoretical foundations of differential and integral calculus. Prerequisite: 221. Strongly recommended for students considering post- graduate study in mathematics.

MAT 323

Introduction to Complex Analysis

1

Study of complex numbers and functions of a complex variable. Topics include algebra and geometry of the complex plane, derivatives, integrals, power series, Laurent series, and residue theory. Prerequisite: 221 or permission. Recommended for students considering graduate study in mathematics.

MAT 324

Algebraic Systems

1

Study of concepts abstracted from algebraic properties of the classical number systems, including groups, rings, fields, order relations, and equivalence relations. Prerequisite: 220 or 243.

MAT 327

Probability & Statistics

1

Calculus-based survey, including axioms of probability, discrete and continuous random variables, standard probability functions (binomial, normal, Poisson, etc.), mathematical expectation, generating functions, and a brief introduction to estimation and hypothesis testing. Prerequisite: 122.

MAT 339

Foundations of Geometry

1

Survey of ancient, classical and modern views regarding the nature of space, the description of spatial structures and the organization of facts about space into deductive theories. Prerequisite: 121.

MAT 343

Discrete Mathematics II

1

Continues the discussion of discrete mathematics introduced in Mat 243. Topics include predicate logic, recurrence relations, graphs, trees, matrices, computational complexity, elementary computability and discrete probability. Prerequisite: 243 or 220.

MAT 359

Introduction to Topology

1

Study of concepts, growing out of and underlying geometry and calculus, which have become important in physics, chemistry, logic, and computer science. Careful development of abstract notions such as topological spaces, continuity, topological equivalence, connectedness, and dimension, and related philosophical and historical matters in mathematics and liberal arts generally. Prerequisite: 121.

MAT 434

Rings and Fields

1

Selected topics, including rings, subrings, integral domains, fields, ideals, quotient rings, ring homomorphisms, polynomial rings, extension fields, finite fields. Prerequisite: 324. Recommended for students considering graduate study in mathematics.

MAT 437

Topics:Probability/Statistics

1

Content varies. Prerequisite: 327. Offered on demand.

MAT 461

Advanced Seminar

1

Student-led inquiry/research in an area of mathematics such as real or complex analysis, topology, algebra, etc. Content varies. May be repeated for credit. Prerequisite: Open to junior and senior math majors.

### Faculty

- Professor of Mathematics and Computer ScienceMathematics
- Professor of MathematicsMathematics
- Professor of MathematicsMathematics
- Associate Professor of Mathematics and Computer ScienceMathematics
- Jeffrey VaughnAdjunct Instructor of MathematicsMathematics
- Barbara WahlProfessor of Mathematics & Computer ScienceMathematics