Mathematics Degrees

MAT 003 – Intermediate Algebra 3 sh
The topics include a review of the real number system, linear equations and applications, linear inequalities and absolute value, graphs and functions, exponents, polynomial functions, factoring, rational functions, root functions, exponential and logarithmic functions. Students who have previously received credit for a higher-numbered mathematics course may not receive credit for this course without permission of the instructor.

MAT 005 – Mathematics for Nurses 1 sh
This course is an introduction to computing techniques used by nurses in hospitals and other clinical situations. Topics include a review of arithmetic and basic computational techniques, standard and apothecary measurement systems, dimensional analysis, and one-factor and multi-factor medication problems. These topics will be examined in depth with a focus placed on understanding the underlying computational techniques. Prerequisite: None.

MAT 017 – Introduction to Mathematics 3 sh
This General Education introductory-level course is intended to acquaint the student with the nature and spirit of mathematics. Topics include set theory, logic, counting methods, probability, statistics, and algebra-based problem-solving with graphical and analytic solutions.

MAT 030 – Survey of Mathematics 3 sh
Sets and logic; number systems; relations and functions; introduction to matrices; linear systems; counting and probability; sequences and limits; introduction to differential and integral calculus.

MAT 040 – Geometry 3 sh
An informal, intuitive study of topics in geometry. Non-metric geometry of the plane and space; measurement; error in measuring; simple closed curves; area; congruence; similarity; graphing in the plane and space; modern geometries; groups of geometric transformations. Open to all majors.

MAT 045 – Women in Mathematics 3 sh
This course examines women who have made significant contributions to the field of mathematics. Both their lives and their work will be explored as well as the gender issues surrounding their endeavors. Furthermore, mathematical topics related to their contributions will be discussed. Prerequisite: 2 years of high school algebra.

MAT 103 – Fundamentals of Math I 3 sh
This is the first course in a two-course sequence that is required for all Elementary Education and Special Education majors. It is not open to other majors. Topics include problem-solving; logic; set theory; mathematical systems; systems of numeration; number theory; equations and inequalities; and properties of whole numbers, integers, rational numbers, and real numbers. MAT 103 is a prerequisite for MAT 104 and ELU 308.

MAT 104 – Fundamentals of Math II 3 sh
This is the second course in a two-course sequence that is required for all Elementary Education and Special Education majors. It is not open to other majors. Topics include informal geometry; measurement; probability; statistics; and computer applications. MAT 103 is a prerequisite for MAT 104. MAT 103 and MAT 104 are prerequisites for ELU 308.

MAT 105 – College Algebra 3 sh
This course is intended for students with an elementary knowledge of algebra who need more work in algebraic topics before taking more advanced mathematics courses. Topics include properties of the real numbers, problem-solving using equations and inequalities, algebraic functions, graphing, and systems of equations. A graphing calculator is required for this course. Prerequisite: Two years of algebra at the high school level.

MAT 106 – Trigonometry 3 sh
This course is intended for students with an elementary knowledge of algebra who need more work in trigonometric topics before taking more advanced mathematics courses. Topics include properties of and operations with functions, inverse functions, exponential and logarithmic functions, angle measurement, trigonometric functions and their inverses, graphing functions, and problem-solving with equations that use the functions covered in the course. A graphing calculator is required for this course. Prerequisite: MAT 105 or its equivalent.

Analysis and Applied Mathematics
In this area, real analysis, harmonic analysis, complex variables, ordinary differential equations, partial differential equations, integral equations, operator theory and all analytical problems originating from applied science are studied. Applications of the research results are employed to solve concrete problems that arise in natural science, engineering, and financial mathematics. Computerized tomography(CT) using the Radon transform and image processing using the wavelets are conspicuous applications of analysis.
Topology
Here, the structures and the properties of manifolds are studied using algebraic, geometric, and combinatorial methods. Active research areas include (i) knots, links, braids, and 3-manifolds (ii) the geometric structures on low-dimensional manifolds including hyperbolic and discrete group theory (iii) 4-manifolds through Seiberg-Witten theory, symplectic and contact structures, and (iv) symmetries of manifolds in terms of group actions on differential manifolds, algebraic varieties, and semi-algebraic sets. In addition applications are effectively being made to computer graphics and non-commutative cryptography, in which braid groups are used.
Geometry
Using differential manifold theory and Riemannian manifolds, those working in geometry study such topics as curvature pinching problems, curvature and group actions, closed geodesics, finiteness theorems, comparison theorems, geometric structure and isometric immersions, harmonic maps and non-linear problems.
Scientific Computational Mathematics
Computational mathematics involves the study of methods of representing complex phenomena as mathematical models and discovering techniques of numerically solving the models. Research is also directed towards theoretical studies based on the analysis and developments of new techniques applicable to science and engineering.
Combinatorics
Combinatorics is an area of mathematics that studies mathematical objects having discrete or combinatorial structures. It involves combinatorial problems from various fields of mathematics and allows for the development of theories about diverse combinatorial objects. Emphasis is put on enumerative combinatorics, graph theory and algebraic combinatorics.
Information Mathematics
Topics studied in this field include Shannon’s information theory, computation theory, complexity theory, Hoffman code, entropy, data compression, error correcting codes, cryptography, and information security.
Financial Mathematics
The area of financial mathematics involves the study and design of mathematical models of financial derivatives and markets using stochastic integral equations or stochastic differential equations. Real data from the markets are used to test mathematical models and the techniques to predict the market movements are studied.
Probability and Statistics
In probability, random phenomena in nature and society are studied rigorously in terms of measure theory. Research emphasis is on stochastic process, martingale, Markov chain, stochastic differential equations, queueing theory for the analysis of telecommunication systems, stochastic control theory and optimization.
In statistics, emphasis is on multivariate statistical analysis, data analysis, learning theory, neural network models, graphic models, time series analysis, Bayesian analysis, parameter estimation, hypothesis verification, regression analysis, etc.

In the master’s program, students go through advanced level mathematical training in preparation to use mathematics after graduation, or they concentrate on the fundamental mathematics required for more advanced study in the doctoral program. Currently about half of the students in the master’s program continue to study mathematics in the doctoral program, while the rest play an active role in industry or government research institutes.

Students learn basics to be experts in Mathematical Sciencess and make plan for their coursework or research according to their own interests. They have opportunities to experience other areas through the various extracurricular activities such as colloquia and exchange programs with foreign universities.

The Department encourages interdisciplinary research with other academic fields. In the master’s program there are many students who have not majored in Mathematical Sciencess for bachelor’s degree. In fact, students with various backgrounds make valuable and creative research environments.

In the doctoral program, students study more advanced mathematics and produce their own new research results. They are well-trained to be competent mathematicians or researchers in industry and government research institutes. Until now, about 70% of Ph.D. produced in the Department have become professors of mathematics, computer science, or related fields, while the rest have been employed in government research institutes or industry.

In the undergraduate program, students take various courses chosen from a variety of courses offered by the Department, according to their interests and career plan, to learn a broad foundation of mathematical knowledge. Every student has an academic advisor who helps in planning coursework, and one can do independent study to build research experience under the direction of a professor specializing on the subject of one’s choice.

The graduates of the Department of Mathematical Sciencess find diverse career paths. Some go on to graduate schools to study and research more mathematics, some take the advantage of applicability of mathematics and enter graduate schools in other fields such as physics, biology, engineering, computer science, finance, business administration and economics, others begin a career in industry related to communication, information security, computers, securities, insurance, finance and banking.

Mathematics is the study on numbers, space, sets and functions with the basic human mental abilities such as classification, calculation, estimation and proof. It is used to abstract and quantify the natural phenomena, and serves as the language of science, essential to understand the law of nature.

As human civilization develops and matures, the role of mathematics continues to increase in its use and importance, not only in the development of the natural sciences and engineering but also in the study of humanities, social studies, economics and related disciplines. In our information society advanced mathematics is essential in many areas such as communication, computer science, information security and finance.

The Department of Mathematical Sciencess has two objectives, research and education. It does research on algebra, analysis, geometry, probability, statistics, topology, bio-mathematics, computational mathematics, financial mathematics, etc. It also emphasizes contribution to the society by producing leading experts in Mathematical Sciencess. To achieve the goal, The Department maintains the highest level of education and research, expands interdisciplinary studies with science, engineering and business administration, stimulates interaction with other universities, research institutes and industry, to induce synergy effects. To contribute to the development of new technology, the Department encourages students to pursue a minor or dual major so that they can be ready for future cooperation with experts from other fields. The Department wishes, by establishing close ties between energetic faculty and creative students, to lead 21st century mathematics of Korea with an effective transfer of mathematical knowledge from faculty to students.

Recently the demand for KAIST graduates majoring Mathematical Sciencess is increasing. Graduates with bachelor’s degree find various career paths, those with master’s degree go mostly into research institutes or areas related to finance, computer science and information, those with Ph. D. take positions in universities, research institutes and industry.

MATH 214 Introduction to Numerical Mathematics (1)
An introduction to elementary numerical methods and their computer implementation. Topics include Newton’s method for one and several equations, interpolating functions, approximating polynomials, numerical differentiation and integration, numerical solutions of linear systems of equations, and numerical solutions of differential equations. Prereq : MATH 151 or equivalent; QL; A.Leahy;

MATH 215 Vector Calculus (1)
A study of vector fields and the calculus of vector differential operators (gradient, divergence, curl, Laplacian), potential functions and conservative fields, line and surface integrals, the theorems of Green, Gauss, and Stokes. Applications. Prereq : MATH 205; QL; Staff

MATH 216 Foundations of Geometry (1)
A study of the axiomatic structure and historical development of two-dimensional geometry, with an emphasis on proofs. Incidence geometry, geometry of flat and curved spaces, projective geometry, and Euclidean models for hyperbolic geometry. Historical implications of the existence of non-Euclidean geometries. Prereq : MATH 152; QL; Staff

MATH 217 Number Theory (1)
A study of the properties of the natural numbers. Prime numbers, divisibility, congruences, Diophantine equations, and applications to cryptography. Prereq : MATH 152; QL; M.Armon;

MATH 218 History of Mathematics (1)
A study of the evolution of mathematical ideas from ancient to modern times. Prereq : MATH 152; QL; A.Leahy;

MATH 227 Introductory Financial Mathematics (1)
An introduction to the key mathematical ideas and techniques that support the two main arms of the area of Financial Mathematics: portfolio optimization and option valuation. The mathematics of personal finance including interest, loans, and annuities, probability modeling for finance, single-period portfolio optimization, utility theory, introduction to the CAPM model, linear programming methods, single-period valuation of futures and options, and multiple time period asset models using Markov chains. Prereq : MATH 205 and MATH 210, or permission of the instructor; K.Hastings;

MATH 230 Differential Equations (1)
A study of equations involving functions and their derivatives. First and second order equations, linear algebra and systems of linear differential equations, numerical and graphical approximations, and elementary qualitative analysis. Prereq : MATH 205; MATH 210 recommended; QL; Staff

MATH 250 Independent Study (1/2 or 1)
Staff

MATH 295 Special Topics (1/2 or 1)
Courses offered occasionally to students in special areas of Mathematics not covered in the usual curriculum.Staff

MATH 300 Mathematical Structures (1)
A rigorous study of the mathematical structures which form the foundation of higher mathematics. Set theory, logic, formal development of the number systems from the natural numbers through the complex numbers, basic algebraic structures (groups, rings and fields), and elementary topological concepts. Prereq : MATH 210 or MATH 230; QL; W; Staff

MATH 311 Scientific Computing (1)
An advanced study of the mathematics of numerical approximation. Error in computation, interpolation, and approximation. Numerical methods of integration, numerical solution to systems of linear equations, ordinary differential equations, and nonlinear equations. Basic notions of computational complexity. Prereq : MATH 210 and some programming experience; QL; A.Leahy;

MATH 313 Topology (1)
A rigorous study of the fundamental ideas of point-set topology. Metric spaces, topological spaces, separation, compactness, connectedness, homeomorphism. Prereq : MATH 300; QL; Staff

MATH 321 Mathematical Statistics I (1)
An advanced study of probability theory. Sample spaces, random variables and their distributions, conditional probability and independence, transformations of random variables. Prereq : MATH 205 and MATH 210; QL; W; K.Hastings;

MATH 322 Mathematical Statistics II (1)
A rigorous study of the theory of statistics with attention to its applications. Point and interval estimation, hypothesis testing, regression and correlation, goodness-of-fit testing, analysis of variance. Prereq : MATH 321; QL; K.Hastings;

MATH 325 Introduction to Operations Research (1)
A rigorous treatment of methods and algorithms for optimization problems, with applications to business and economics and other areas. Networks, linear programming, Markov chains, Poisson processes, queueing theory, dynamic programming. Prereq : MATH 321; QL; K.Hastings;

MATH 327 Advanced Financial Mathematics (1)
Continued study of the key mathematical ideas and techniques that support the two main arms of the area of Financial Mathematics: portfolio optimization and option valuation. Cox-Ross-Rubinstein model of asset prices in discrete time, Brownian motion and stochastic integral models for continuous time problems, optimal portfolio consumption problem, exotic options, dynamic programming approach to valuation of derivative assets, Black-Scholes option valuation. Statistical estimation of the parameters of the asset price process will also be discussed. Prereq : MATH 227 and MATH 321, or permission of the instructor; QL; K.Hastings;

MATH 331 Analysis I (1)
A rigorous study of the concepts of continuity, differentiation, integration, and convergence in one variable. Prereq : MATH 300 or permission of the instructor; QL; W; D.Schneider;

MATH 332 Analysis II (1)
A continuation of MATH 331. A rigorous study of the concepts of calculus in higher dimensions. QL; D.Schneider;

MATH 333 Complex Analysis (1)
A rigorous study of analytic functions and their properties. The Cauchy-Riemann equations, Cauchy’s Theorem, Taylor and Laurent expansions, the calculus of residues, conformal mappings, and harmonic functions. Prereq : MATH 331; QL; D.Schneider;

MATH 341 Abstract Algebra I (1)
A rigorous study of the fundamental notions of abstract algebra. Groups, rings, integral domains, and fields. Prereq : MATH 300 or permission of the instructor; QL; W; Staff

MATH 342 Abstract Algebra II (1)
A continuation of MATH 341. A rigorous study of more advanced topics such as Galois theory, modules and vector spaces. QL; Staff

MATH 350 Independent Study (1/2 or 1)
Staff

MATH 360 Research in Mathematics I (.0 or 1/2)
MATH 360-361 is a sequence of two courses in which students engage in guided research of a topic not normally covered elsewhere in the curriculum. Student produce written reports of their work, and do public oral presentations. MATH 361, if taken for 1/2 credit must build on the experience of another course in mathematics numbered 211 or above. Prereq : MATH 300. Mathematical Finance majors who have not taken MATH 300 must have taken MATH 321; Staff

MATH 361 Research in Mathematics II (1/2 or 1)
Prereq : MATH 360 or permission of instructor; Total credit for MATH 360-361 not to exceed 1 credit; O; Staff

MATH 395 Topics in Advanced Mathematics (1/2 or 1)
Courses offered occasionally to students in special areas of Mathematics not covered in the usual curriculum. May be repeated for credit.; Staff

MATH 399 Seminar in Mathematics (1)
An advanced study of a special topic in mathematics not substantially covered in the regular curriculum. Emphasis on student presentations and independent writing and research. Students submit a major paper and give a public lecture. Recent topics include optimization theory and the history of mathematics. Prereq : MATH 300 and senior standing or permission of the instructor; O; QL; Staff

MATH 400 Advanced Studies (1/2 or 1)
See College Honors Program. O; Staff

MATH 121 Mathematical Ideas (1)
An introduction to the history and concepts of elementary mathematics. Topics may include: properties of number systems, geometry, analytic geometry, mathematical modeling, and probability and statistics. Designed for non-majors. QL: MATH 121 cannot simultaneously satisfy proficiency and QL requirement; Staff

MATH 125 Mathematics for Elementary School Educators (1)
A theoretical study of the mathematical concepts taught in elementary school mathematics. Topics include sets, functions, number systems, number theory, statistics, and the role and use of technology. Prereq : at least one course in Educational Studies; QL; Staff

MATH 131 Functions (1)
An introduction to the concept of a function and its graph. Polynomial and rational functions, logarithmic and exponential functions, and trigonometric functions. Examination of the relationship between algebraic and graphical formulations of ideas and concepts. Prereq : 3 years college preparatory mathematics or permission of the instructor; QL; Staff

MATH 140 , MATH 141 Functions and Calculus I-II (1)
An introduction to the theory and applications of the differential calculus including a review of concepts from precalculus. Limits, continuity and differentiation of functions of one variable, with applications. Students successfully completing MATH 141 are prepared for MATH 152. Prereq : three years of college preparatory mathematics; MATH 140 and MATH 141 together cover all the calculus material treated in MATH 151. Credit cannot be earned for MATH 151 in addition to credit for either MATH 140 or MATH 141. MATH 141 carries MNS Foundation credit. QL; Staff

MATH 141 Functions and Calculus II (1)
A continuation of MATH 140. Students successfully completing MATH 141 are prepared for MATH 152. MNS; Prereq : MATH 140; MATH 140 and MATH 141 together cover all the calculus material treated in MATH 151. Credit cannot be earned for MATH 151 in addition to credit for either MATH 140 or MATH 141. QL; Staff

MATH 151 Calculus I (1)
An introduction to the theory and applications of the differential calculus. Limits, continuity, differentiation, approximation, and optimization. MNS; Prereq : MATH 131 or three years of college preparatory mathematics, including trigonometry; QL; Staff

MATH 152 Calculus II (1)
A continuation of MATH 151. An introduction to the theory and applications of the integral calculus as well as an introduction to infinite series and parametric equations. MNS; Prereq : MATH 141 or MATH 151; QL; Staff

MATH 160 Statistics (1)
A study of the acquisition, interpretation, and presentation of data. Statistical graphics and summary statistics, random sampling, elementary probability, random variables and distributions, introduction to interval estimation and hypothesis testing. MNS; Prereq : MATH 131 or equivalent, or permission of the instructor; QL; Staff

MATH 175 Discrete Mathematics (1)
A study of discrete mathematical structures. Logic and proof, set theory, relations and functions, ideas of order and equivalence, and graphs. MNS; Prereq : MATH 151 or equivalent, or CS 141 together with MATH 131 or equivalent; QL; Staff

MATH 180 Combinatorics (1)
The study of problems for which the number of possible solutions is large but finite. Developing, proving, analyzing and applying algorithms to find optimal solutions. Algorithmic graph theory, counting techniques, discrete probability, difference equations. Prereq : MATH 151 or equivalent, or CS 141 together with MATH 131 or equivalent; QL; Staff

MATH 205 Calculus III (1)
An introduction to the calculus of functions of several variables and vector-valued functions. Limits, continuity, differentiation, and multiple integration. MNS; Prereq : MATH 152 or permission of the instructor; QL; D.Schneider;

MATH 210 Linear Algebra I (1)
A study of the fundamental properties and applications of finite dimensional vector spaces, linear transformations, and matrices. Spanning, independence, bases, inner products, orthogonality, eigenvalues and eigenvectors, diagonalization. MNS; Prereq : MATH 152 or permission of the instructor; QL; D.Schneider;

MATH 211 Linear Algebra II (1)
A continuation of MATH 210. A more abstract study of vector spaces and linear transformations. Spectral and Jordan decomposition theorems. Applications. Prereq : MATH 205 and MATH 210; QL; D.Schneider;

Requirements for the major in Mathematics

10 credits in the Mathematics Department as follows:
Core courses: MATH 152, MATH 205, MATH 210, MATH 300
Electives: 6 additional courses as follows: At most one of MATH 175 and MATH 180; At least 5 courses numbered above MATH 210, at least two of which are numbered above Math 300
Research Experience: Each student must complete a research project leading to a written and oral presentation. This requirement may be fulfilled through MATH 361, MATH 399, or an honors project, and must be certified by the department chair. Full credits earned in this experience may apply to the elective credit requirement.

With permission of the chair, up to two credits in related studies outside the department may be counted toward electives in the major.

Requirements for the major in Financial Mathematics

10.5-11 credits as follows:
Core courses: MATH 152, MATH 205, MATH 210
Introductory Financial Mathematics: MATH 227
Mathematical Statistics: MATH 321, MATH 322
Economics: 2 courses from: ECON 110, ECON 301, BUS/ECON 333, BUS 211, BUS 212
Related coursework: 1 additional course from: MATH 211, MATH 214, MATH 215, MATH 230, MATH 311, MATH 325, CS 142, CS 205
Advanced Financial Mathematics: MATH 327
Research Experience: Each student must complete a research project leading to a written and oral presentation. This requirement may be fulfilled through MATH 361, MATH 399, or an honors project, and must be certified by the department chair

Students who major in Financial Mathematics and minor in Business and Management may count no more than 3 courses simultaneously in both programs.

Requirements for the minor in Mathematics

5 credits in the department as follows:
MATH 152 or MATH 214, MATH 205, MATH 210
Two additional mathematics courses numbered above MATH 170, with at least one chosen from: MATH 211, MATH 216, MATH 217, MATH 218, MATH 300

Requirements for the minor in Financial Mathematics

6 credits in the department as follows:
MATH 152, MATH 205 and MATH 210
MATH 227
MATH 321
MATH 327

A distinctive feature of the mathematics major at Knox is the importance given to effective communication. In all courses students are expected to write clearly. In the course “Mathematical Structures” and in Senior Seminar, classes literally write their own textbooks. Students also are regularly asked to give professional-quality presentations.

Mathematics students begin with a solid foundation in calculus, linear algebra and mathematical structures before proceeding to a variety of advanced courses and independent work. Some majors undertake a College Honors project, which involves a year of research on a mathematical topic, a paper and an oral defense. Recent honors projects have dealt with topics such as fundamental solutions for partial differential equations and options pricing.

As a “capstone” experience, mathematics majors are required to participate in the independent study of a topic of current interest and produce a talk on the topic.

The department also offers a major and minor in Mathematical Finance.

At Knox, mathematics is marked by a commitment to analytic rigor, an emphasis on clear understanding, the ability to communicate effectively with others, and an excitement about the unlimited possibilities within this field of knowledge.

Today, the pleasure and the excitement of studying mathematics are intensified by the capacities of modern computers, which have helped bring new developments within the reach of the serious undergraduate. Knox has been at the forefront in capturing the power of computers, both for class assignments and in research.