Mathematics
A degree in mathematics is an excellent means of preparation for postcollege years, whether a student intends to work in business or industry, teach, or pursue graduate studies. At Cal Lutheran we provide a broad and challenging program designed to develop fundamental skills and to prepare students for lifelong learning. The program features small classes with an emphasis on facultystudent interaction, classroom technology to facilitate learning, computer labs for student exploration and discovery, and a focus on interdisciplinary applications. Faculty mentors assist students in reaching their academic and career goals. Students are challenged to explore the many facets of mathematics and its applications through creative and critical thinking. Departmental space is set aside as a study and resource area for majors. Free tutoring for lower division courses is provided in the Math Lab.
The faculty encourage students to apply their mathematical knowledge by participating in internships, carrying out independent projects, and tutoring in the Math Lab. Students synthesize and extend their mathematical experiences in the senior capstone course. Other opportunities include participating in paid summer research programs across the nation, spending a semester studying mathematics abroad, preparing for and competing in national mathematicsrelated contests, and preparing posters and presentations for seminars and regional or national conferences.
Employers in the public and private sectors seek generalists with critical thinking skills who are capable of adapting to a wide variety of situations. Graduates in mathematics are prepared in this manner and can work in many career fields. These include computer science, engineering, actuarial science, education, business, finance and the natural sciences. Along with finding excellent employment opportunities, Cal Lutheran math majors have also been accepted for graduate studies at top universities throughout the United States.
Students who wish to register for a mathematics course must meet the necessary prerequisites, as stated in the Schedule of Classes and the Undergraduate Catalog. Students unsure of whether they meet the prerequisites should contact a mathematics faculty member. Courses numbered 400 and above are best taken after or concurrently with a 300level course.
All Cal Lutheran students are required to meet the Mathematical Reasoning Proficiency under Core 21. Students who meet the proficiency requirement may still need to meet specific mathematics requirements for their majors
Major Requirements
Only mathematics courses numbered 200 or above earn credit toward a major in mathematics.
Bachelor of Science in Mathematics
45 credits minimum, 25 credits upper division.
MATH 241  Discrete Mathematics  4 
MATH 251  Calculus I (preferred)  4 
or MATH 245  Applied Calculus  
MATH 252  Calculus II  4 
MATH 261  Calculus III  4 
MATH 320  Elementary Mathematical Analysis  4 
or MATH 382  Number Theory  
MATH 420  Real Analysis  4 
or MATH 425  Abstract Algebra  
One 4credit elective (upper or lower divsion)  4  
Four 4credit upper division mathematics classes (one class may be 3credits instead)  1516  
MATH 475  Capstone  2 
Total Hours  4546 
Required Supporting Courses
PHYS 211/211L  Mechanics and ThermodynamicsCalculus and Mechanics and ThermodynamicsLab  5 
PHYS 212/212L  Electricity, Magnetism, and Optics  and Electricity, Magnetism Optics Lab  5 
Computer Programming course at the 200level or above (choice must be approved by Math Advisor)  
CSC 210  Introduction to Computer Programming  4 
or CSC 205  Programming for Scientists  
Total Hours  14 
Recommended Supporting Courses
MATH 474  Capstone Preparation (strongly recommended)  2 
CHEM 151/151L  General Chemistry and General Chemistry Lab  5 
CHEM 152/152L  General Chemistry II and General Chemistry II Lab  5 
Total Hours  12 
Bachelor of Arts in Mathematics
41 credits minimum, 21 credits upper division.
MATH 241  Discrete Mathematics  4 
MATH 251  Calculus I (preferred)  4 
or MATH 245  Applied Calculus  
MATH 252  Calculus II  4 
MATH 261  Calculus III  4 
Take at least two of the following three courses  8  
Elementary Mathematical Analysis  
Geometry  
Number Theory  
One 4credit math elective (upper or lower division)  4  
Three additional 4 credit upper division mathematics classes (one of which may be only 3credits)  1112  
MATH 475  Capstone  2 
Total Hours  4142 
Required Supporting Courses
One mathematical perspectives course (can be a Math upper divsion elective, must be approved by Math advisor)  34  
Complete one of the following two course sequence options  910  
Physics Option  
Mechanics and ThermodynamicsCalculus and Mechanics and ThermodynamicsLab  
Electricity, Magnetism, and Optics  and Electricity, Magnetism Optics Lab  
Economics Option  
General Economics  
One of the following 400level Economics classes  
Intermediate MacroEconomics  
Intermediate MicroEconomics  
or ECON 450  Econometrics  
Total Hours  1214 
Recommended Supporting Courses
MATH 474  Capstone Preparation (Strongly Recommended)  2 
A course in Computer Programming at the 200level or above  34  
Introduction to Computer Programming  
or CSC 205  Programming for Scientists  
CHEM 151/151L  General Chemistry and General Chemistry Lab  5 
CHEM 152/152L  General Chemistry II and General Chemistry II Lab  5 
Total Hours  1516 
Minor in Mathematics
20 credits minimum, 8 credits upper division.
Only mathematics courses numbered 200 or above earn credit toward a minor in mathematics. Either MATH 245 or MATH 251 (preferred) may be counted toward the minor, but not both.
MATH 251  Calculus I  4 
or MATH 245  Applied Calculus  
MATH 252  Calculus II  4 
Two 4credit upper division mathematics classes  8  
Select one of the following:  4  
Discrete Mathematics  
Calculus III  
Differential Equations  
4credit upper division mathematics class  
Total Hours  20 
Requirements for the Mathematics Single Subject Program
Students considering a career as a teacher of mathematics in a California high school or middle school should consider completing the CLU Mathematics Single Subject Program which is an approved subject matter program for the California Commission on Teacher Credentialing. Completion of this program allows a student to enroll directly in a teaching credential program upon graduation. Program requirements most closely match the B.S. in Mathematics degree, include an entrance interview after completing Calculus II, and a portfolio defense at the end. Students interested in entering the program should discuss program requirements with the director of the Mathematics Single Subject Program.
Honors in Mathematics
Nomination Process
Students interested in completing Departmental Honors must be nominated by a Math faculty member prior to their final year. This normally will occur three semesters before graduation, but might occur two semesters before. In order to be eligible for nomination a student must satisfy all three of the following requirements:

A Math GPA of at least 3.5 with no semester grade below a B in any upper division Math course,

An overall GPA of 3.0,

2 upper division Math courses either completed or in progress.
Selection Process
Once nominated, a student takes MATH 474 Capstone Prep and develops a proposal for an Honors Project. The project proposal must follow the guidelines for Capstone in Mathematics projects but must be for a yearlong project that holds the promise of completing publishable results. After the oral and written project proposals have been reviewed, the Math faculty will determine if a student’s project is worthy of being selected as an Honors project. Moreover, by the time the candidate is selected he/she must also have completed at least 2 Upper Division Math courses with a grade of B or higher in both, and have at least 1 additional upper division Math course completed or in progress.
Completion of Departmental Honors
To complete Departmental Honors students must successfully pass all of the following courses:

MATH 474  Capstone Prep 2 credits (taken spring of Junior year)

MATH 475 – Capstone2 credits (taken fall of Senior year)

MATH 497  Honors Research3 credits (taken Spring of Senior year)
This is equivalent to one year of mentored research experience, plus one semester of research preparation in the Capstone Prep course. The final project will be presented in three venues: a written thesis, an oral presentation, and a poster presentation. The advisor in conjunction with Math faculty will review the project at the end of the Capstone course to determine if the student may proceed with the Honors Research course. At the end of the Honors Research course they will again confer to determine if the project meets the standards of an honors project.
Courses
Lower Division
MATH 110. Intermediate Algebra. (4).
This course covers equations and inequalities, polynomials, rational and radical expressions, exponents, graphing linear equations and inequalities, linear systems, exponential and logarithmic functions, and places extensive emphasis on word problems. This course is appropriate for students with Math SAT 530 or below.
MATH 115. Finite Mathematics. (4).
This course studies mathematics and models in the social sciences including logic, sets, families of functions, and an introduction to descriptive and inferential statistics. Recommended for social science majors. Prerequisite: MATH 110 or a Math SAT of 540 or above.
MATH 120. Concepts Underlying Arithmetic. (4).
This course is designed for the prospective elementary school teacher, and emphasis is on developing a deep understanding of the mathematical ideas necessary for superb teaching of elementary school mathematics. Communication of these ideas through appropriate language and the use of diagrams, patterns, and everyday objects is a critical feature of the class. Students are expected to work in cooperative groups during class, and to make presentations on a regular basis. Topics include number sense, representations of numbers, number systems, creating and analyzing algorithms for arithmetic operations, proportional reasoning, problem solving, algebraic thinking, and current California state math standards. Issues of access and pedagogy are addressed both individually and in the context of the mathematical ideas. This course does not satisfy the Core 21 Mathematical Reasoning Requirement. Prerequisites: MATH 110 or a Math SAT of 540 or above.
MATH 128. Topics in Liberal Arts Math. (4).
This course engages the students in an exploration of the nature of mathematics as well as a selection of mathematical topics chosen to illustrate why mathematics is one of the original liberal arts. An emphasis is placed on problem solving and communication of ideas through writing and class discussions. The nature of mathematics as well as two, three and fourdimensional geometry, and probability and statistics will be included each semester. Other topics will be chosen by the instructor. Prerequisite: MATH 110 or Math SAT 540 or above.
MATH 145. Business Mathematics. (4).
This course studies the elementary models of mathematics in business settings including the use of functions to model concepts such as revenue and profit, as well as interest and annuities. Additional topics include linear regression, decision trees, and an introduction to probability and statistics. Recommended for Business majors. Prerequisite: MATH 110 or Math SAT 540 or above.
MATH 151. Precalculus. (4).
This course studies real numbers, equations, inequalities and polynomial, rational, exponential, logarithmic and trigonometric functions. Prerequisite: MATH 110 or Math SAT 540 or above.
MATH 151S. Supplemental Instr: 151S. (0).
This is the Supplemental Instruction Blackboard Platform attached to MATH 151. As a student enrolled in this section, you are automatically enrolled in the attached Supplemental Instruction Blackboard Platform. Supplemental Instruction (SI) is an academic support program designed to improve student success in challenging foundation courses. SI is a wellresearched program that has been shown to improve students' letter grades by a half to a full grade, with consistent participation. With the SI model, a SI Leader (a student who has successfully completed the course with a B+ or better in the past, and who has an overall GPA of 3.0 or higher) is embedded into the course, attending all course meetings. The SI Leader then facilitates the scheduling and running of group SI study sessions throughout the week. There will typically be three one hour SI Sessions or two 90 minute SI Sessions per week. The SI Blackboard Platform is hosted by your SI Leader, who will utilize it to take confidential attendance at SI Sessions, to make general announcements to the class members, and to share helpful resources and study materials for SI Sessions. Participation in the SI study sessions is completely optional and always free, and you may come to as many or as few sessions as you would like over the semester. Your course professor does not receive any information about attendance, so you can be certain that your participation will be kept confidential.
MATH 231. Statistics for the Sciences. (4).
This course introduces the principles, methods of reasoning, summarization, analysis and preparation of scientific data. Computer laboratory sessions are included to facilitate data handling and analysis. Topics include sampling and experimental design, descriptive statistics, probability, statistical inference and interpretation of results, simple regression and ANOVA. Prerequisite: MATH 151 or Math SAT 620 or above.
MATH 241. Discrete Mathematics. (4).
Topics include set theory, number systems, the nature of proofs, recursion, algorithms, graph theory and problem solving. This course is required for computer science and computer information systems majors. Prerequisite: MATH 151.
MATH 245. Applied Calculus. (4).
This course examines methods of mathematics used in business and economics, with a focus on problem solving and applications. It includes the ideas of differential calculus, including applications to marginal analysis (cost, revenue, profit), the elasticity of demand, and optimization. Concepts of integration up through substitution are included. Optimization is further examined through systems of linear equations and matrices, linear programming and a brief introduction to game theory. Required for Business Majors. Prerequisite: MATH 115, MATH 145, MATH 151 or Math SAT 620 or above.
MATH 251. Calculus I. (4).
Studies the concepts of the limit, the derivative and the definite integral of functions of one variable. Included are applications to rates and areas, differentials and basic modeling. Prerequisite: MATH 151 or Math SAT 620 or above.
MATH 251S. Supplemental Inst: Math 251. (0).
This is the Supplemental Instruction Blackboard Platform attached to MATH 251. As a student enrolled in this section, you are automatically enrolled in the attached Supplemental Instruction Blackboard Platform. Supplemental Instruction (SI) is an academic support program designed to improve student success in challenging foundation courses. SI is a wellresearched program that has been shown to improve students' letter grades by a half to a full grade, with consistent participation. With the SI model, a SI Leader (a student who has successfully completed the course with a B+ or better in the past, and who has an overall GPA of 3.0 or higher) is embedded into the course, attending all course meetings. The SI Leader then facilitates the scheduling and running of group SI study sessions throughout the week. There will typically be three one hour SI Sessions or two 90 minute SI Sessions per week. The SI Blackboard Platform is hosted by your SI Leader, who will utilize it to take confidential attendance at SI Sessions, to make general announcements to the class members, and to share helpful resources and study materials for SI Sessions. Participation in the SI study sessions is completely optional and always free, and you may come to as many or as few sessions as you would like over the semester. Your course professor does not receive any information about attendance, so you can be certain that your participation will be kept confidential.
MATH 252. Calculus II. (4).
This course continues the study of differentiation and integration begun in Calculus I. Introduces indefinite integration and applications of the definite integral. Differential equations and elementary methods to solve them are presented, along with direction fields and some modeling applications. Includes Taylor polynomials and series. Students will use a computer algebra system to engage with material in the course. Prerequisites: MATH 251.
MATH 261. Calculus III. (4).
Calculus III extends the concepts of calculus to a multivariable perspective. Topics such as functions, derivatives, integrals and various coordinate systems are used to explore change modeled by two or more variables. Vector algebra and vector fields are introduced to study the motion of objects. Students will use a computer algebra system to engage with material in the course. Prerequisite: MATH 252. (offered in fall).
MATH 265. Differential Equations. (4).
Students will formulate differential equations to model phenomena, solve these equations when possible and analyze these equations when solutions are not possible. Students will study single variable differential equations and systems, and applications of these in areas such as physics, chemistry and ecology. Analytical, graphical, and numerical methods will be explored. Prerequisite: Math252. Recommended prerequisite: MATH261 (offered in spring).
MATH 282. Selected Topics. (4).
MATH 282C. ST: Select Topic (core). (14).
Select Topic approved for Core requirement.
MATH 285. Travel Seminar. (14).
Upper Division
MATH 320. Elementary Mathematical Analysis. (4).
An introduction to mathematical analysis emphasizing conjecture and proof. Content includes elementary logic and quantifiers, manipulations with sets, relations and functions, properties of the real number system, supremums and infimums, sequences and limits of sequences, and the topology of the real line. The course will introduce students to the concepts and techniques of mathematical proof. Prerequisite: MATH 252, Recommended: MATH 241.
MATH 331. Data Analysis With R. (4).
This course studies the analysis of complex data sets in the statistical programming language R. Topics include an introduction to programming in R, data cleaning, descriptive statistics and graphics, probability models, hypothesis testing, confidence intervals, linear and logistic regression, classification, and cluster analysis. Students will learn to communicate their statistical results by critiquing journal articles and producing their own written analyses. Required prerequisites: MATH 231 or MATH 241 or MATH 251.
MATH 341. Graph Theory/Combinatorics. (4).
The course extends upon concepts introduced in Discrete Mathematics. Graph theory concepts include isomorphism, planarity, Eulerian circuits, and colorings. Network optimization concepts include minimum spanning trees, shortest path, traveling salesperson problem, maximum flow, and matching. Concepts in combinatorics include permutations, combinations, arrangements, distribution, binomial identities, generating functions, and recurrence relations. Students will be required to write proofs for theorems and pseudocode for algorithms.Prerequisite: MATH 241.
MATH 343. Linear Algebra. (4).
An introduction to solving systems of linear equations through the use of concepts such as vector spaces, linear transformations, matrices, eigenvalues and eigenvectors. Students will enhance mathematical communication skills through reading and writing proofs and will explore interdisciplinary applications of the theory of linear algebra in projects and computer laboratory assignments. Prerequisite: MATH 252. Recommended: MATH 261.
MATH 352. Probability and Statistics I. (4).
This course covers topics including methods of data description, probability theory, a study of several discrete and continuous distributions, the central limit theorem, estimation of parameters, confidence intervals and hypothesis testing. Prerequisite: MATH 252. Recommended: MATH 261.
MATH 381. Geometry. (4).
This course primarily investigates the integration of geometries on the plane, sphere and hyperbolic plane. An emphasis is placed on experiencing the meanings in the geometry. Student investigations, smallgroup learning and writing assignments will be used to explore geometrical ideas. The history and culture of mathematics, particularly as reflected by the development of geometrical understanding, will be threaded through the course. Prerequisite: MATH 252. Recommended: MATH 261 and MATH 343.
MATH 382. Number Theory. (4).
This course focuses on the properties of integers and the history of the discovery of these properties. Topics include fundamental theorems on divisibility, primes and congruences, as well as numbertheoretical functions, Diophantine equations, quadratic reciprocity and Fermat's Last Theorem. This course will introduce students to the concepts and techniques of mathematical proof. Prerequisite: MATH 252 or consent of instructor. Recommended: MATH 241.
MATH 420. Real Analysis. (4).
A study of the real number system, set theory, sequences, functions, continuity, differentiation and RiemannStieltjes integration, with an emphasis on developing the ability to communicate mathematically. Prerequisite: MATH 261 and either MATH 382 or MATH 320 (preferred).
MATH 425. Abstract Algebra. (4).
Studies the theory of integers, groups, rings, fields and polynomials. Prerequisite: MATH 241 and either MATH 382 (preferred) or MATH 320.
MATH 450. Complex Variables. (4).
Topics include complex numbers and functions, analytic functions, differentiation, integration, series, contour integrals and conformal mapping. Prerequisite: MATH 261 and one other upper division mathematics course.
MATH 452. Probability and Statistics II. (4).
This course extends the concepts of probability and statistics through a multivariable perspective. Students study statistical models through topics such as experimental design, regression, analysis of variance, contingency tables and order statistics. Data handling and analysis are conducted with the aid of statistical software. Prerequisites: MATH 261 and MATH 352.
MATH 474. Capstone Preparation. (2).
Whether in industry, graduate school, or in your capstone project, skills in formulating answerable questions, identifying relevant sources, and locating helpful ideas is important. This course investigates the diversity of mathematical topics, skills for researching the topics, and the components of a project proposal. The course culminates in a written and oral presentation of a project proposal. Prerequisite: Mathematics major or minor and Junior standing. (offered in spring).
MATH 475. Capstone. (2).
The capstone in mathematics is intentionally openended. The focus of the course centers on the mathematics majors designing and carrying out individual projects suited to their interests and postgraduation goals. Weekly class meetings will be run in seminar fashion: each student will be expected to present at least one report on a) the culture of mathematics, b) the relationship between mathematics and other disciplines or career avenues or c) a moral/ethical issue related to mathematics. Prerequisite: senior standing.
MATH 482. Selected Topics. (14).
MATH 482C. ST: Select topic (core). (14).
Select Topic approved for core requirement.
MATH 485. Seminar. (24).
MATH 490. Independent Study. (14).
MATH 492. Internship. (14).
(graded P/NC only).
MATH 496. Directed Research. (13).
MATH 497. Honors Research. (3).
Faculty
Professors
Karrolyne Fogel
Michael Gagliardo
John Villalpando
Associate professor
Nathan Carlson
Assistant professors
Christopher Brown
Delil Martinez
Lecturer
Ryan DeMoss