Mathematics and Computational Sciences

Human Services

See listing under Behavioral Sciences

Mathematics and Computational Sciences

Dr. Joe A. Stickles, Jr., Chair

Department of Mathematics Faculty

Full-Time: Christine A. Harshman, Cassidy F. Krause, Eun-Joo Lee, Daniel R. Miller, Emily J. Olson, James V. Rauff, Joe A. Stickles, Jr., Paula R. Stickles

The Department of Mathematics and Computational Sciences includes the disciplines of mathematics, actuarial science, data science, mathematics education, and computer science. The department offers a major in mathematics and minors in mathematics and actuarial science. Students who major in mathematics may choose a concentration in actuarial science, data science, or secondary mathematics education. The department also offers a major and a minor in computer science.

The curriculum is structured to meet the overlapping needs of students who fall in one or more of the following categories: • those who intend to pursue graduate work in mathematics and related fields; • those who will apply mathematics in the natural sciences, social sciences, business or other areas; • those who plan to become actuaries; • those who plan to become data scientists; • those who plan to become high school mathematics teachers; and • those who plan to become computer scientists.

Mathematics Major Requirements

Students planning to major in mathematics may earn either a B.A. or B.S. degree. Mathematics majors should be prepared to enroll in MA140 or a higher course during the first semester at Millikin. MA098, MA109, MA110, MA112, MA113, MA115, and MA130 do not count toward a major or minor.

All majors are required to complete the common foundation courses. This foundation is comprised of the following five mathematics courses. MA140. Calculus I MA208. Discrete Mathematics MA240. Calculus II MA303. Linear Algebra MA304. Probability

The department may waive one or more of the foundation course requirements for students with advanced high school mathematics preparation. There are four options for students interested in a mathematics major.

1. Mathematics 2. Mathematics with emphasis in Actuarial Science. The actuarial science track is identified by the Society of Actuaries' website as an advanced curriculum undergraduate actuarial science program (UCAP-AC). Additionally, some courses in this track have been approved by the Society of Actuaries to earn Validation by Educational Experience (VEE) . 3. Mathematics with emphasis in Data Science 4. Mathematics with Secondary Education Certification. The secondary mathematics education program is an Illinois State Board of Education Approved Program for the Preparation of Educational Personnel in Illinois Institutions of Higher Education.

Below are the additional requirements for each of the four options.

Mathematics Major

Students interested in immediate employment in a mathematical area or in further study in mathematics should elect this option. In addition to the foundation requirements, students must take

CS135. Introduction to Computer Science CS235. Introduction to Data Science MA305. Differential Equations MA340. Calculus III MA403. Abstract Algebra MA440. Advanced Calculus MA499. Senior Seminar

Two courses selected from

MA313. Numerical Analysis MA314. Mathematical Statistics MA320. History of Mathematics MA324. Theory of Interest MA420. Mathematical Logic MA472. Internship MA491, 492,493,494. Independent Study

A minimum of 15 additional hours in a discipline to which mathematics is applied. Students’ areas of application will be made in consultation with their academic advisors.

Mathematics Major with Emphasis in Actuarial Science

The actuarial science track is identified by the Society of Actuaries' website as an advanced curriculum actuarial science program. Additionally, some courses in this track have been approved by the Society of Actuaries to earn Validation by Educational Experience (VEE) . Students interested in becoming an actuary should elect this option. In addition to the foundation requirements, students must take

CS135. Introduction to Computer Science CS235. Introduction to Data Science MA230. Regression Analysis and Time Series MA314. Mathematical Statistics* MA324. Theory of Interest MA340. Calculus III MA499. Senior Seminar AC230. Introduction to Financial Statements* AC240. Principles of Managerial Accounting* EC100. Principles of Maoeconomics* EC110. Principles of Microeconomics* FI340. Introduction to Financial Management*

*Approved VEE Courses at Millikin University The following courses have been approved by the Society of Actuaries for VEE at Millikin University: Economics - EC100 and EC110 Accounting and Finance – AC230, AC240, and FI340 Mathematical Statistics - MA314

Students who have completed this option will be prepared to take the first two Actuarial Examinations (1/P and 2/FM) of the Casualty Actuarial Society and the Society of Actuaries.

Mathematics Major with Emphasis in Data Science

Data scientists find and interpret rich data sources and are skilled in mathematics, statistics, and computer science. Students electing this option will take courses and do research in mathematics, computer science, and information systems. Working with large data sets, they will build mathematical models, use advanced statistical methods, and implement machine learning algorithms to classify and predict. In addition to the foundation requirements, students must take

MA230. Regression Analysis and Time Series MA314. Mathematical Statistics MA340. Calculus III MA499. Senior Seminar IS221. Programming Fundamentals IS240. Foundations of Information Systems IS321. System Analysis & Design IS370. Database Application Development IS470. Business Intelligence and Big Data CS135. Introduction to Computer Science CS235. Introduction to Data Science CS308. Theory of Computation CS337. Algorithms and Data Structures CS342. Artificial Intelligence

One course selected from

AT110. Introduction to Digital Media BU230/CO230. Business Conversations BU250/EN210. Professional and Technical Writing

Mathematics Major with Secondary Education Certification

The secondary mathematics education program is an Illinois State Board of Education Approved Program for the Preparation of Educational Personnel in Illinois Institutions of Higher Education. Students interested in teacher certification should elect this option. In addition to the foundation requirements, students must take

MA301. College Geometry MA320. History of Mathematics MA403. Abstract Algebra MA425. Methods of Teaching Secondary and Middle School Mathematics, Grades 5 through 12 MA471. Internship in Methods of Teaching Mathematics Two courses selected from:

MA305. Differential Equations MA313. Numerical Analysis MA314. Mathematical Statistics MA340. Calculus III MA420. Mathematical Logic MA440. Advanced Calculus MA491, 492, 493, 494. Independent Study

Teacher certification in the State of Illinois mandates students earn a C- or better in all required mathematics and education courses. Teacher certification also requires specific coursework in education and other areas. See the School of Education section for details. Students should consider preparation in a second teaching field to increase the breadth of their knowledge and the probability of finding a teaching position upon graduation. Students may select to add a concentration in Special Education, English as a Second Language, or Bilingual Education to their education major. Completion of this concentration will meet the requirements of adding this area as an added endorsement of to the teaching license.

Minor in Mathematics

A minor in mathematics is an excellent complement to majors in the natural sciences, social sciences and business. To receive a minor in mathematics a student must successfully complete the following course of study.

MA140. Calculus I MA240. Calculus II MA208. Discrete Mathematics MA303. Linear Algebra

At least two other mathematics courses numbered 300 or higher.

Minor in Actuarial Science

A minor in actuarial science is well-suited for students who are interested in exploring a career as an actuary. The required courses cover material for two actuarial exams, and one course satisfies the Mathematical Statistics VEE requirement. These courses are:

MA140. Calculus I MA230. Regression Analysis and Time Series MA240. Calculus II MA304. Probability MA314. Mathematical Statistics MA324. Theory of Interest

Mathematics Courses (MA) (Credits)

MA098. Intermediate Algebra (3)

Further study of algebra concepts and techniques with applications. Includes functions and graphs, systems of equations, systems of linear inequalities, radical functions and equations, complex numbers, quadratic functions, exponential and logarithmic functions, and conic sections. Does not satisfy quantitative reasoning requirement of the MPSL. A student who has scored a 3 or higher on the mathematics placement exam or who has earned credit in a

quantitative reasoning course may not earn credit for MA098.

MA109. Finite Mathematics (3)

Analysis, description and solution of problems arising in business, computer science, and natural and social sciences. Emphasis on mathematical models whose construction and solution involve a finite number of clearly defined steps. Includes an introduction to finite probability and elementary statistics. Topics selected from matrices, systems of linear equations, linear inequalities, linear programming, functions and their graphs, Markov processes, game theory, decision theory, mathematics of finance and networking.

MA110. College Algebra (3)

Study of basic operations; equations and inequalities; polynomial, exponential, and logarithmic functions and graphs; matrices; determinants; sequences; series; mathematical induction; theory of equations; and selected topics from combinatorics.

MA112. Mathematics Content for Elementary School Teachers I (3)

This first course is designed to help prepare a prospective elementary school teacher in mathematics. It includes a study, from a problem-solving standpoint, of many topics covered in elementary school mathematics such as natural numbers, whole numbers, rational and irrational numbers, arithmetic operations on these numbers, systems of numeration, language and nature of inductive and deductive reasoning, elements of set theory, and elementary number theory.

MA113. Mathematics Content for Elementary School Teachers II (3)

This second course is designed to help further prepare a prospective elementary school teacher in mathematics. It includes a study, from a problem-solving standpoint, of many topics covered in elementary school mathematics such as geometry, measurement, probability and statistics.

MA115. Trigonometry (3)

Study of the trigonometric functions and their properties, applications to triangles and other geometric figures, and also graphs of trigonometric functions and inverse trigonometric functions. Additional material selected from polar coordinates and complex numbers.

MA130. Elementary Probability and Statistics with Spreadsheets (3)

Introduction to descriptive statistics, relevant concepts in probability (including random variables and their distributions), sampling, inferential statistics, hypothesis testing, and regression. Applications to business are emphasized, and spreadsheets are used as an analytical tool.

MA140. Calculus I (4)

Differential and integral calculus from the symbolic, graphical and numerical perspectives. Topics covered include: concepts of limit, continuity, derivative and integral; applications of the derivative as rate of change, slope and solving max-min problems.

MA208. Discrete Mathematics (3)

Introduces basic techniques of proof and combinatorial problem solving. Topics include graphs, trees, logic, applied combinatorics, and number theory.

MA230. Regression Analysis and Time Series (3)

This course is an introduction to major methods of applied statistics and time series. Topics include simple and multiple regression, analysis of variance and covariance, model specification and residual analysis, nonparametric inference, experimental design, and multivariate analysis. Introduces modeling time series data using smoothing techniques, regression and autoregressive models.

MA240. Calculus II (4)

Applications of definite integral and Fundamental Theorem of Calculus, methods of integration, power series, Taylor series, Fourier series, use of differential equations to model real-life applications.

MA301. College Geometry (3)

Elements of plane and solid geometry treated from a problem-solving approach, historical development of geometry, parallelism and symmetry, area and volume, and non-Euclidean geometry.

MA303. Linear Algebra (3)

Matrices, linear systems, finite dimensional vector spaces, vector geometry, linear transformations, quadratic forms.

MA304. Probability (3)

Combinatorial analysis, probability axioms, discrete and continuous random variables and their distributions, central limit theorem, and multivariate distributions. Prepares students for Exam P of the Society of Actuaries.

MA305. Differential Equations (3)

Elementary differential equations and applications including linear differential equations with constant coefficients and first order systems, higher order differential equations and applications. Existence and uniqueness theorems. Numerical techniques.

MA313. Numerical Analysis (3)

Iterative methods for approximating numerical solutions to systems of equations, polynomials, integral and differential equations. Includes matrix manipulation and error analysis.

MA314. Mathematical Statistics (3)

Point estimation, interval estimation, hypothesis testing, and analysis of variance.

MA320. History of Mathematics (3)

A study of major developments in the history of mathematics and in the mathematical contributions of non-Western cultures. The interplay between mathematics and culture is emphasized.

MA324. Theory of Interest (3)

This course is designed to prepare students for Exam FM that is administered by the Society of Actuaries. Topics include compound interest formulas, annuities, perpetuities, amortization schedules, bonds, and other securities.

MA325. Mathematical Physics (3)

We will discuss applications of mathematics to various areas of physics. Topics may include vector calculus, linear algebra, differential equations, series solutions to differential equations, Fourier series, special functions, and calculus of variations. The primary audience for this course is sophomore and junior majors who are preparing to take Analytical Mechanics, Electrodynamics, or Quantum Mechanics, although applied mathematics majors may find the course useful.

MA340. Calculus III (4)

Introduction to calculus of several variables, partial derivatives, multiple and iterated integrals, and vector functions.

MA403. Abstract Algebra (3)

An introduction to abstract algebra. Includes basic ideas and theorems about groups, rings, integral domains, and fields.

MA420. Mathematical Logic (3)

An introduction to mathematical logic and metamathematics. Includes predicate calculus, proof theory, formal axiomatic theories, consistency, completeness, and decidability.

MA425. Methods of Teaching Secondary and Middle School Mathematics, Grades 5-12 (3)

Microteaching and structured classroom participation required. The course focuses on teaching standards based mathematics content with the inclusion of appropriate technologies. Required for high school Illinois Mathematics Teacher Certification.

MA434. Mathematical Finance (3)

This course is designed to prepare students for Exam IFM that is administered by the Society of Actuaries. Topics include forwards, futures, option spreads, binomial option pricing, Black-Scholes option pricing, option Greeks, and interest rate derivatives.

MA440. Advanced Calculus (3)

A rigorous treatment of fundamental analysis concepts. Includes topology of the real number system, limits, continuity, sequences, differentiability, and integrability.

MA444. Life Contingencies (3)

This course is designed to prepare students for Exam LTAM that is administered by the Society of Actuaries. Topics include survival models for single and multiple life states, present value random variables, calculation of premiums, annuity and insurance reserves, and pensions and retirement benefits.

MA454. Life Contingencies II (3)

This course is the second course in the sequence designed to prepare students for Exam LTAM that is administered by the Society of Actuaries. Topics include survival models for single and multiple life states, present value random variables, calculation of premiums, annuity and insurance reserves, and pensions and retirement benefits.

MA471. Internship in Methods of Teaching Mathematics (3)

Students learn methods of teaching mathematics in a classroom situation under the supervision of a member of the department. Includes methods of course organization, presentation, and assessment and the use of technology in teaching mathematics.

MA472. Internship (3)

An on-the-job professional experience working for an organization, business or University department during an academic semester. A supervised work experience in which the superior student’s mathematical background is used in an actual working environment.

MA491, 492, 493, 494. Independent Study (2 or 3 per Semester)

Advanced study in a topic chosen jointly by student and instructor. Some recent topics have included introduction to topology, set theory, partial differential equations, complex analysis, projective geometry, and complexity theory.

MA499. Senior Seminar (3)

Research in mathematics. Students create and present a research project under the direction of a member of the mathematics faculty.

Computer Science Major Requirements

The computer science major provides the opportunity for students to develop skills in writing algorithms to solve problems across academic disciplines; to design and write software in a variety of languages; to understand the fundamental concepts and issues in data structures, systems administration, computer architecture, web programming, networking, machine learning, and artificial intelligence; and to develop the ability to communicate their knowledge effectively.

This program prepares majors for postgraduate study in computer science and for entry-level positions as computer professionals in industry. Students planning to major in computer science may earn either a B.A. or B.S. degree. A computer science major should plan to enroll in Computer Science 135 or a higher course during their first semester at Millikin. Placement in the proper computer science course will be determined in consultation with the faculty advisor based on the student’s previous record in computer science.

To complete a major in computer science, students must successfully complete the following course of study.

CS135. Introduction to Computer Science CS208. Discrete Mathematics for Computer Science CS235. Introduction to Data Science CS300. Advanced Discrete Mathematics CS308. Theory of Computing CS337. Algorithms and Data Structures CS499. Senior Seminar IS221. Programming Fundamentals IS240. Foundations of Information Systems IS311. IT Infrastructure IS321. Systems Analysis and Design IS370. Database Application and Development MA140. Calculus I MA240. Calculus II MA303. Linear Algebra

Two electives taken from CS342. Artificial Intelligence CS430. Computer Architecture CS460. Topics in Computer Science

CS491. Independent Study in Computer Science IS322. Web/Mobile Application Development IS470. Business Intelligence and Big Data MA313. Numerical Analysis

Minor in Computer Science

The Computer Science Minor offers students in all majors the opportunity to develop skills in writing algorithms to solve problems and to understand the fundamental concepts of computer science. To receive a minor in computer science a student must successfully complete the following course of study.

CS135. Introduction to Computer Science CS208. Discrete Mathematics for Computer Science CS235. Introduction to Data Science CS308. Theory of Computation CS337. Algorithms and Data Structures.

Two additional courses, one of which must bear a CS or IS prefix, selected from

CS300. Advanced Discrete Mathematics CS342. Artificial Intelligence IS221. Programming Fundamentals IS321. Systems Analysis and Design IS470. Business Intelligence and Big Data MA420. Mathematical Logic Mathematics majors with a Data Science emphasis may not earn a Computer Science Minor.

Computer Science Courses (CS) (Credits)

CS135. Introduction to Computer Science (3)

A first computer science course taken by students in mathematics and science, as well as those seeking the dual-degree program in computer science. Topics include fundamentals of computation and algorithmic problem-solving, data types, control structures, basic graphics, the object-oriented programming paradigm and applications. Introduces a high-level programming language such as Python.

CS208. Discrete Mathematics for Computer Science (3)

Introduces essential discrete mathematics for computer science. Topics include sets, logic, functions, relations, sequences, matrices, discrete probability, graphs, applied number theory, and algorithm analysis.

CS235. Introduction to Data Science (3)

A continuation of CS135. Includes computational complexity, visual display of data, recursion, optimization, stochastic programming, Monte Carlo simulation, Bayesian inference, nearest neighbor classification, and k-means clustering. Programs are implemented in a high-level programming language such as Python.

CS300. Advanced Discrete Mathematics (3)

An examination of discrete mathematics topics of particular relevance to computer scientists. Includes computational complexity, cryptography, discrete probability, graphs, trees, networks, petri nets, Boolean algebra and combinatorial circuits, data representation, and instruction set architectures.

CS308. Theory of Computation (3)

An introduction to the theory of computation emphasizing formal languages, automata, and computability. Includes computational complexity and NPcompleteness.

CS337. Algorithms and Data Structures (3)

Study of algorithms and data structures.

CS342. Artificial Intelligence (3)

Introduction to the theory and practice of artificial intelligence. Topic areas selected from heuristic search techniques, knowledge representation, symbolic reasoning, fuzzy logic, planning, learning, natural language processing, expert systems, genetic programming, intelligent agents, swarm intelligence, and neural networks.

CS360. Topics in Computer Science (3)

Elective topics in computer science. Examples include natural language processing, human-computer interaction, mobile computing, embedded computing, neural networks, crypto-currency, game design, programming languages, and cryptography.

CS430. Computer Architecture (3)

This course provides an introduction to the design of computer architecture. Topics include memory allocation, type representation, CPU performance, computer arithmetic, memory management, control structures, and input/output devices.

CS491. Independent Study in Computer Science (3)

In depth study of a particular area or topic in computer science.

CS499. Senior Seminar (3)

Students will design, implement, and test a substantial computer solution for a third-party stakeholder. Grading will include periodic progress reports, evaluations by instructor and the stakeholder(s), and a final presentation.

Engineering Science Major Requirements

Engineering science is an interdisciplinary major designed to provide students with a diverse set of skills that will allow them to apply engineering principles to areas such as computing, finance, manufacturing, medicine, and politics.

To earn a degree in engineering science, students are required to complete the engineering science core courses. Upon completion of those courses, students have two options. Students who wish to stay at Millikin for four years to complete their undergraduate degree may choose to complete an additional 16 hours of coursework at the 300-level from the list below and complete any additional graduation requirements. The second option is to complete a dual degree program with one of our partnership institutions. Students completing this option typically complete three years of coursework at Millikin and two years at the partner school. For a list of our current dual degree partnerships, go to http://millikin.edu/STEM.

Engineering Science core (52-53 hours) BI105, Ecology and Evolution BI155. Ecology and Evolution Lab BI200. Genetics CH121. General Chemistry I CH122. General Chemistry II CH151. General Chemistry Laboratory I CH152. General Chemistry Laboratory II CS135. Introduction to Computer Science CS235. Introduction to Data Science MA140. Calculus I MA240. Calculus II MA305. Differential Equations MA340. Calculus III PY151. University Physics I PY152. University Physics II PY171. Physics Laboratory I PY172. Physics Laboratory II PY262. Experimental Physics I – Electronics

Choose one of the following: BI240. Analysis of Biological Data CH232/253. Analytical Chemistry and Analytical Chemistry Laboratory MA230. Regression Analysis and Time Series MA314. Mathematical Statistics

Select one of the following options:

Option 1: Select at least 16 additional hours from the list below: BI301. Comparative Anatomy BI407. Molecular Genetics CH301. Organic Chemistry I CH302. Organic Chemistry II CH304. Physical Chemistry I CH353. Physical Chemistry Laboratory I CH354. Physical Chemistry Laboratory II CS300. Advanced Discrete Mathematics CS308. Theory of Computing CS337. Algorithms and Data Structures CS342. Artificial Intelligence MA303. Linear Algebra MA304. Probability PY352. Classical Dynamics PY362. Experimental Physics II PY403. Electrodynamics I PY404. Electrodynamics II

With approval of the Engineering Science coordinator, another 300-level course in biology, chemistry, computer science, mathematics, or physics may be substituted for one (or more) of the above options.

Option 2: Complete coursework at a dual degree partnership school and transfer back to Millikin at least 16 hours of 300-level coursework approved by the Natural Science and Mathematics Division and any additional hours necessary to satisfy Millikin’s degree requirements.