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 CLU 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, CLU 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 CLU 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 ThermodynamicsCalculus Lab  5 
PHYS 212/212L  Electricity, Magnetism, and Optics  Calculus and Electricity, Magnetism, and Optics  Calculus 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 ThermodynamicsCalculus Lab  
Electricity, Magnetism, and Optics  Calculus and Electricity, Magnetism, and Optics  Calculus Lab  
Economics Option  
General Economics and General Economics Lab  
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 500 or
below.
MATH 115. Finite Mathematics. (4).
This course studies the elementary models in
business and social sciences including systems of
linear equations and inequalities, matrices,
interest, annuities and an introduction to
probability and statistics. Recommended for
business and social science majors. Prerequisite:
MATH 110 or Math SAT 510 or above.
MATH 120. Algorithms for Arithmetic. (2).
This course is designed for the prospective
elementary school teacher, and emphasis is on
understanding the deep mathematical ideas
necessary for superb teaching of elementary
school mathematics. Communication and group work
are expected. Topics include number sense,
representations of numbers, number systems,
creating and analyzing algorithms for arithmetic
operations, recognition and analysis of patterns,
problem solving, algebraic thinking, and issues
of access and pedagogy. Prerequisite: MATH 110 or
Math SAT 510 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 510 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 500 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 510 or above.
MATH 231. Biostatistics. (4).
This course introduces the principles, methods of
reasoning, summarization, analysis and
presentation of biological and biomedical 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 clinical trials. Prerequisite:
MATH 151 or Math SAT 600 or above.
(offered in spring).
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 or Math SAT 600 or above.
(offered in fall).
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 or Math SAT 600 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. A weekly
computer lab is a key component of the course.
Prerequisite: MATH 151 or Math SAT 600 or
above.
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. A weekly computer
lab is a key component of the course.
Prerequisite: 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. A weekly computer laboratory
session facilitates exploration, visualization
and reinforcement of the main topics of the
course. Prerequisite: MATH 252. (offered
in fall).
MATH 265. Differential Equations. (4).
Focuses on the formulation of appropriate
mathematical models to represent phenomena, the
solution (when possible) of such equations, and
understanding and interpreting the solutions of
these equations. Graphical and analytical methods
will be explored, as will numerical techniques.
Prerequisite: MATH 252. Recommended:
MATH 261. (offered in spring).
MATH 282. Selected Topics. (4).
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 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 440. Mathematical Methods of Physics. (4).
Mathematics with a focus to meet the needs of
students with a major or minor in physics or
engineering disciplines. Topics include: complex
variables, linear algebra, coordinate
transformations, vector analysis, Fourier series
and transforms; Laplace transforms, the Dirac
delta function, Green functions, calculus of
variations and solution techniques for partial
differential equations with specific applications
to Laplace's equation. Prerequisites: MATH 261
and PHYS 212. Recommended: MATH 265.
(Crosslisted with PHYS 440).
MATH 450. Complex Analysis. (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 471. Mathematical Modeling. (4).
A speakingintensive introduction to modeling
techniques, synthesizing concepts and methods
learned in previous courses. Applications will be
chosen from various disciplines (particularly
science, social science, business and education),
environmental resource issues and
scheduling/allocation. Techniques used will
include computer simulation, game theory,
difference equations and/or differential
equations and probabilistic models or statistical
models. Prerequisites: MATH 265.
Recommended prerequisites: MATH 352 and a
course in computer programming.
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 485. Seminar. (24).
MATH 490. Independent Study. (14).
MATH 492. Internship. (14).
(graded P/NC only).
MATH 497. Honors Research. (3).
Associate professors
Karrolyne Fogel  
Hala King  
John Villalpando 
Assistant professors
Chris Brown  
Nathan Carlson  
Michael Gagliardo 
Adjunct professors
James English  
Sue Martinez  
Rashid Sani  
Christina Soderlund  
Jorge Soto  
Angela Wilkins 