## Academic Requirements

Coe is an exciting place to be a student in the mathematical sciences. We have an active community of students and faculty participating in a variety of pursuits. The department offers a complete range of courses, with majors and minors available in both mathematics and computer science, as well as courses in statistics for additional breadth. We are dedicated to the belief that the mathematical sciences and the habits of mind that they engender are perfect components of a fine liberal arts education.

The department's curriculum is carefully designed to meet the needs of a range of students' interests and abilities. We pride ourselves on the individual attention we provide through small classes and extra contact with faculty outside the classroom. Our course offerings are wide enough and flexible enough to suit each individual in a personalized atmosphere, starting with the basics and progressing to a level suitable both for positions in industry and for continuing on to graduate study.

Cross (Chair), Herron, Hostetler, C. Van Niewaal, White.

### Mathematics Major

- MTH-135 Calculus I
- MTH-145 Calculus II
- MTH-215 Foundations of Advanced Mathematics
- MTH-255 Calculus III
- MTH-265 Linear Algebra
- MTH-385 Modern Algebra I
- CS-125 Computer Science
- One of the following:

MTH-415 Real Analysis I

MTH-445 Complex Analysis - Three of the following: STA-315 Probability and Statistics I

STA-325 Probability and Statistics II

MTH-305 Advanced Geometry

MTH-325 Differential Equations

MTH-395 Modern Algebra II

MTH-415 Real Analysis I (if not used to satisfy #8)

MTH-425 Real Analysis II

MTH-445 Complex Analysis (if not used to satisfy #8)

MTH-455 Mathematical Modeling

MTH-505 Set Theory and Topology

MTH-705 Special Topics

MTH-8_5 Independent Study

### Mathematics Minor

- MTH-135 Calculus I
- MTH-145 Calculus II
- MTH-215 Foundations of Advanced Mathematics
- Three of the following:

STA-315 Probability and Statistics I

STA-325 Probability and Statistics II

MTH-255 Calculus III

MTH-265 Linear Algebra

MTH-305 Advanced Geometry

MTH-325 Differential Equations

MTH-385 Modern Algebra I

MTH-395 Modern Algebra II

MTH-415 Real Analysis I

MTH-425 Real Analysis II

MTH-445 Complex Analysis

MTH-455 Mathematical Modeling

MTH-505 Set Theory and Topology

MTH-705 Special Topics

MTH-8_5 Independent Study

### Elementary Education Emphasis in Mathematics

- MTH-135 Calculus I
- MTH-145 Calculus II
- MTH-215 Foundations of Advanced Mathematics
- MTH-265 Linear Algebra
- MTH-305 Advanced Geometry
- TA-100 Statistical Foundations and STA-110 Inferential Statistics

NOTE: A course in statistics and a course in geometry are required for the Iowa teaching endorsement in mathematics at either the elementary or secondary school level. Students planning to teach should consult with faculty in the teacher education department.

### Courses in Mathematics

MTH-105 Mathematics in Today’s World

An introduction to contemporary mathematical thinking with emphasis on its connections to society. Logical thinking and the ability to read critically are interwoven with elementary mathematical skills. The course concentrates on discussions about mathematics —about its nature, its content, and its applications to a variety of topics, such as management science, social choice, and the geometry of size and shape. This course is appropriate for a varied audience. Some ability in arithmetic, geometry, and elementary algebra is assumed. This course does not satisfy any of the requirements for a major or minor in the mathematical sciences.

MTH-115 Algebra and Trigonometry

A pre calculus course in algebra, trigonometry, and the elements of analytic geometry. These topics are studied in the context of polynomial, rational, exponential, logarithmic, and trigonometric functions.

MTH-135 Calculus I

An introduction to the concepts of limits, continuity, differentiation of elementary functions, applications, definite and indefinite integrals, and the Fundamental Theorem. Prerequisite: three years of secondary school mathematics, Algebra and Trigonometry (MTH-115), or consent of instructor.

MTH-145 Calculus II

Further study of the techniques of differentiation and integration, the calculus of exponential, logarithmic and trigonometric functions, sequences, series, and applications. Prerequisite: Calculus I (MTH-135) or consent of instructor.

MTH-215 Foundations of Advanced Mathematics

A survey of material common to all advanced study of mathematics, including elements of formal logic, axiomatic set theory, induction, relations, functions, cardinality, and various other topics in discrete mathematics. This course is specifically intended to serve both as a transition to upper-division mathematics courses and also as a survey of some areas of mathematics important for future teachers of mathematics and related fields. Prerequisite: Calculus I (MTH-135) or consent of instructor.

MTH-255 Calculus III

Further study of curves, surfaces, power series, partial derivatives, iterated and multiple integrals, and an introduction to differential and integral vector calculus. Prerequisite: Calculus II (MTH-145) or consent of instructor.

MTH-265 Linear Algebra

A study of the elementary concepts of vector spaces, including matrix algebra, basis and dimension, inner products, linear transformations. Prerequisites: Calculus II (MTH-145) and Foundations of Advanced Math (MTH-215) or consent of instructor.

MTH-305 Advanced Geometry

A course designed to give the student an introduction to the modern approaches to geometry at an advanced level. Topics include foundations, Euclidean, projective, and non-Euclidean geometries. Prerequisites: Calculus II (MTH-145) and Foundations of Advanced Math (MTH-215) or consent of instructor.

MTH-325 Differential Equations

The theory, solution, techniques, and applications of elementary types of ordinary differential equations. Prerequisite: Calculus III (MTH-255) or consent of instructor.

MTH-385 Modern Algebra I

A rigorous introduction to advanced algebra. Topics include mappings, operations, groups, rings, fields, integral domains, and homomorphisms. Prerequisite: Linear Algebra (MTH–265) or consent of instructor.

MTH-395 Modern Algebra II

A continuation of Modern Algebra I (MTH 385), including homomorphisms, permutation groups, symmetry, unique factorization domains, quotient rings, and field extensions. Prerequisite: Modern Algebra I (MTH-385). (Offered on an occasional basis)

MTH-415 Real Analysis I

A rigorous introduction to selected topics in analysis. Topics selected from number systems, Euclidean spaces, metric spaces, limits, continuity, derivatives, and integrals. Prerequisites: Calculus II (MTH-145) and Foundations of Advanced Math (MTH-215).

MTH-425 Real Analysis II

A continuation of Real Analysis I (MTH-415), including a study of such topics as Riemann Stieltjes and Lebesque integration, series and series expansions. Prerequisite: Real Analysis I (MTH-415). (Offered by arrangement)

MTH-445 Complex Analysis

An introduction to the theory, techniques, and applications of functions of a complex variable. Topics include elementary and analytic functions, limits, differentiation, integration, series, mappings, and applications. Prerequisite: Calculus III (MTH-255) or consent of instructor.

MTH-455 Mathematical Modeling

An introduction to the application of mathematical techniques used in the solution of real world problems. These techniques include interpolation, ordinary differential equations, taylor series expansions, curve fitting, matrix inversion, numerical differentiation, and integration. Prerequisites: Computer Science I (CS-125), Foundations of Advanced Math (MTH-215), and Differential Equations (MTH-325) or consent of instructor.

MTH-505 Set Theory and Topology

A rigorous introduction to abstract set theory and to metric and topological spaces, including a discussion of such topics as separation, connectedness, and compactness. Prerequisites: Calculus II (MTH-145) and Foundations of Advanced Math (MTH-215) or consent of instructor.

MTH-705 Special Topics

An opportunity to study current and topical material unavailable through the regular catalog offerings. Prerequisites: Calculus II (MTH-145) and Foundations of Advanced Math (MTH-215) or consent of instructor.

MTH-8_5 Independent Study

An opportunity for independent and intensive study in mathematics. Prerequisite: appropriate background courses depending on the nature of the work planned and consent of department.

MTH-895 Internship in Mathematics

Investigation of a career area related to the student’s interest in mathematics. A minimum of 140 hours on-site experience is required. S/U basis only. Supervision by a faculty member of the department in cooperation with the Director of Internships. This course does not satisfy any of the requirements for a major or minor in mathematics. Prerequisites: junior standing and consent of department.

### Courses in Statistics

STA-100 Statistical Reasoning I—Statistical Foundations

A hands-on introduction to the use of statistical techniques. Provides a foundation for statistical analysis and introduces the basic concepts involved in data collection and presentation. (0.5 course credit) (Offered first 7 weeks of Term)

STA-105 Probability: A World of Chance

An introduction to probability and its applications in our world. This hands-on course examines how probability techniques can be used to understand topics in science, government, recreation, and communication. Bizarre events in everyday life are also discussed. This course is appropriate for a varied audience. Some ability in arithmetic and elementary algebra is assumed. This course does not satisfy any of the requirements for a major or minor in the mathematical sciences.

STA-110 Statistical Reasoning IIA- Inferential Statistics

A continuation of Statistical Reasoning I (STA-100), presenting a broad range of data analysis techniques. Topics covered include hypothesis testing, confidence intervals, Chi-square tests, and regression. Emphasis is on a project-based approach to analyzing data. Prerequisite: Statistical Reasoning I (STA-100) or consent of instructor. (0.5 course credit) (Offered second seven weeks of Term)

STA-130 Statistical Reasoning IIB- Experimental Design

A continuation of Statistical Reasoning I (STA-100), with an emphasis on Analysis of Variance designs. Topics covered include factorial, nested, and hierarchical models. Coursework uses a project-based approach to analyzing data. Prerequisite: Statistical Reasoning I (STA-100) or consent of instructor. (0.5 course credit) (Offered second seven weeks of Term)

STA-315 Probability and Statistics I

A calculus-based introduction to the mathematical theory of probability and statistics. Topics include enumeration techniques, Bayes’ theorem, random variables, discrete and continuous distributions, expectation, moment-generating functions, and sampling distribution theory. Prerequisites: Calculus II (MTH-145) and Foundations of Advanced Mathematics (MTH-215) or consent of instructor.

STA-325 Probability and Statistics II

A continuation of Probability and Statistics I (STA- 315), presenting the theory behind inferential statistics. Topics include point and interval estimation, hypothesis tests, regression, analysis of variance, and nonparametric methods. Prerequisite: Probability and Statistics I (STA-315) or consent of instructor.

### Computer Science Major

- CS-125 Computer Science I
- CS-225 Computer Science II
- CS-325 Computer Organization and Operating Systems
- CS-345 Data Structures and Algorithms
- CS-365 Discrete Structures
- CS-425 Programming Languages
- MTH-135 Calculus I
- MTH-215 Foundations of Advanced Mathematics
- Three of the following:

CS-335 Machine Architecture and Assembly Language

CS-355 Advanced Object Oriented Programming

CS-405 Software Engineering

CS-435 The Theory of Computation

CS-455 Introduction to Database Systems

CS-475 Computer Communications

CS-485 Principles of Computer Graphics

CS-495 Introduction to Compilers

CS-7_5 Special Topics

CS-8_5 Independent Study

### Computer Science Minor

- CS-125 Computer Science I
- CS-225 Computer Science II
- MTH-135 Calculus I
- MTH-215 Foundations of Advanced Mathematics
- CS-325 Computer Organization and Operating Systems
- Two of the following: CS-335 Machine Architecture and Assembly Language

CS-345 Data Structures and Algorithms

CS-355 Advanced Object Oriented Programming

CS-365 Discrete Structures

CS-405 Software Engineering

CS-425 Programming Languages

CS-435 The Theory of Computation

CS-455 Introduction to Database Systems

CS-475 Computer Communications

CS-485 Principles of Computer Graphics

CS-495 Introduction to Compilers

CS-7_5 Special Topics

CS-8_5 Independent Study

### Elementary Education Emphasis in Computer Science

- CS-125 Computer Science I
- CS-225 Computer Science II
- MTH-135 Calculus I
- MTH-215 Foundations of Advanced Mathematics
- CS-325 Computer Organization and Operating Systems
- One additional course in computer science

### Courses in Computer Science

CS-105 Computers and Society

An examination of the impact of emerging computer technologies on western culture. Topics include computer ethics, intellectual property rights, the transformation of work, electronic communities, free speech, privacy, and security. This course does not satisfy any of the requirements for a major or minor in the mathematical sciences.

CS-125 Computer Science I

An introduction to computer science with an emphasis on programming and problem solving. Topics include selection control, iteration, subprograms, algorithms, arrays, and records. Students experiment with basic concepts during regularly scheduled laboratory sessions.

CS-225 Computer Science II

Continuation of CS-125, focusing on the design and implementation of complex programs. This course covers the basics of recursion, pointers, and dynamically allocated data structures. Other topics include classic algorithms, efficiency analysis, abstract data types, and the software development life cycle. Prerequisite: Computer Science I (CS-125).

CS-325 Computer Organization and Operating Systems

Introduces the organization and structure of major hardware components of computers. Assists the student in understanding the mechanics of information transfer and control within computer systems and provides the fundamentals of logic design. Operating systems principles and the interrelationships between the operating system and the architecture of computing systems are included. Prerequisite: Computer Science II (CS-225).

CS-335 Machine Architecture and Assembly Language

An introduction to basic computer organization and programming at the assembly-level. Topics include digital logic, machine-level representation of data, and assembly-level machine organization. Prerequisites: Computer Science II (CS-225) and Foundations of Advanced Mathematics (MTH-215).

CS-345 Data Structures and Algorithms

An introduction to the definition, implementation, and applications of basic data structures and their operations. Topics include abstract data types, recursive algorithms, complexity analysis, sorting and searching, and problem-solving strategies. Prerequisite: Computer Science II (CS-225).

CS-355 Advanced Object Oriented Programming

A further investigation of the role of classes and data abstraction in the design and implementation of software systems. Topics include object-oriented 90 design, inheritance, and polymorphism. Prerequisite: Computer Science II (CS-225).

CS-365 Discrete Structures

Study of the mathematics integral to computer science. Topics include binary-related number systems and internal representation of numbers, recursion and recurrence relations, analysis of algorithms, graphs and trees, logic circuits and simple automata. Prerequisites: Computer Science II (CS-225) and Foundations of Advanced Mathematics (MTH-215).

CS-405 Software Engineering

An introduction to the principal models that govern the design and implementation of large software systems. Topics include the software development process, specifications, verification, and validation. Prerequisite: Data Structures and Algorithms (CS-345) or consent of instructor.

CS-425 Programming Languages

An introduction to the various features of programming languages and how these features support software development. Topics include data and control abstractions, program correctness, programming in the large, and language design. Prerequisite: Data Structures and Algorithms (CS-345) or consent of instructor.

CS-435 The Theory of Computation

An introduction to the classical and contemporary theory of computation. Coverage includes the theory of automata and formal languages, computability by Turing machines, uncomputability, and computational complexity. Prerequisite: Discrete Structures (CS-365) or consent of instructor.

CS-455 Introduction to Database Systems

A study of the concepts and structures necessary to design and implement a database management system. Students review the current literature concerning database technology and design and implement a simple database system with limited functions. Prerequisites: Computer Science II (CS-235) and Foundations of Advanced Mathematics (MTH-215) or consent of instructor.

CS-475 Computer Communications

An introduction to the study of computer networks and data communications. Topics include network topology, data link control, network protocols, transmission, error control, and security. Prerequisites: Computer Science II (CS-225) and Foundations of Advanced Mathematics (MTH-215) or consent of instructor.

CS-485 Principles of Computer Graphics

An introduction to the fundamentals of computer graphics. Topics include user interface design, input/ output devices, and basic graphics concepts. Prerequisite: Data Structures and Algorithms (CS-345) or consent of instructor.

CS-495 Introduction to Compilers

An introduction to the design and organization of compilers. The major phases of a compiler (lexical analysis, parsing, code generation, and optimization) are examined. Prerequisite: Data Structures and Algorithms (CS-345) or consent of instructor.

CS-7_5 Special Topics

An opportunity to study current and topical material unavailable through the regular catalog offerings. Prerequisite: Data Structures and Algorithms (CS-345) or consent of instructor.

CS-8_5 Independent Study

An opportunity for independent and intensive study in computer science. Prerequisites: appropriate background courses, depending on the nature of the work planned, and consent of department.

CS-895 Internship in Computer Science

Investigation of a career area related to the student’s interest in computer science. A minimum of 140 hours on-site experience is required. S/U basis only. Supervision by a faculty member of the department in cooperation with the Director of Internships. This course does not satisfy any of the requirements for a major or minor in computer science. Prerequisites: junior standing and consent of department.