# Mathematics

Mathematics is the study of patterns, both quantitative and spatial. As such, it is the key to understanding our natural and technical world. Through the study of mathematics, students develop skills in problem solving, critical thinking and clear, concise writing.

The Department of Mathematics offers courses which serve as a fundamental part of a liberal education and as a basis for work in other disciplines. In addition, the department offers a complete major program providing opportunities for a deeper study of mathematics. Mathematics majors pursue a wide range of career options, including work in teaching, business, industry and government service. Many mathematics majors choose to continue their studies with graduate work in mathematics, statistics, computer science or other fields which require significant mathematical background, such as economics or science.

The department also provides opportunities for independent study and research. Collaborative student/faculty research projects have been conducted in the areas of mathematical modeling, chaos theory, dynamical systems, statistics, real analysis, complex analysis, linear algebra, algebra, representation theory, geometry and bioinformatics.

Study abroad opportunities are available in Budapest, Hungary and Aberdeen, Scotland. In addition, majors can study off-campus at a variety of domestic locations such as Oak Ridge National Laboratory.

## Majors

The Department of Mathematics offers both a Bachelor of Science and a Bachelor of Arts in mathematics. Many of our majors are double majors or minors in areas such as chemistry, physics, computer science and economics. We also have majors who have a second major or minor in areas such as music and English. About half of our mathematics majors become teachers. We offer a Mathematics Secondary Education Major for students intending to become middle school or high school mathematics teachers. We also offer a Mathematics Elementary Education Major for students going into elementary or middle school teaching.

### Bachelor of Arts Degree

The requirement for a Bachelor of Arts degree in mathematics is a plan of study designed in consultation with a departmental advisor, and includes a total of at least 34 credits in mathematics as follows:

- MA 280, 331 and 341 must be included
- Additional credits chosen from the following courses: MA 126, 131, 132, 231, 232,
and all courses numbered above 300
*except*323 and 324 - No more than 16 credits from courses numbered 232 and lower shall be counted towards the 34 required credits

See individual course descriptions for prerequisites.

### Bachelor of Science Degree

The requirement for a Bachelor of Science degree in mathematics is a plan of study designed in consultation with a departmental advisor, and includes a total of 60 credits of courses from the natural science division of which at least 39 credits must be in mathematics as follows:

- MA 280, 331 and 341 must be included
- Additional credits chosen from the following courses: MA 126, 131, 132, 231, 232,
and all courses numbered above 300
*except*323 and 324 - No more than 16 credits from courses numbered 232 and lower shall be counted towards the 39 required credits

See individual course descriptions for prerequisites.

### Mathematics Elementary Education

In partnership with the Hope College Department of Education, the Department of Mathematics offers a teaching major in the elementary level for certification through the State of Michigan.

The requirement for a major in mathematics with elementary teaching emphasis is a plan for study designed in consultation with a departmental advisor, and includes a total of at least 34 credits in mathematics as follows:

- Complete MA 126 or MA 131
- Complete MA 132, 205, 206, 231, 280, 311, 312, 321 and 351
- Complete at least 4 additional credits selected from MA 207, MA 208, and GEMS courses centered on mathematical topics (GEMS 100 or 105).

### Mathematics Secondary Education

In partnership with the Hope College Department of Education, the Department of Mathematics offers a teaching major in the secondary level for certification through the State of Michigan.

The requirement for a Bachelor of Arts degree in mathematics for those intending to become middle school or high school mathematics teachers is a plan of study designed in consultation with a departmental advisor, and includes a total of at least 34 credits in mathematics as follows:

- MA 132, 231, 280, 311, 312, 321, 331, 341, and 351 must be included
- Additional credits chosen from the following courses: MA 126 or 131, MA 232 and all
courses numbered above 300
*except*323 and 324 - No more than 16 credits from courses numbered 232 and lower shall be counted towards the 34 required credits
- MA 323 and 324 must also be taken (
*this counts as education credit, and does not count toward the 34 mathematics credits*).

## Minors

The Department of Mathematics offers both a Bachelor of Science and a Bachelor of Arts in mathematics. Many of our majors are double majors or minors in areas such as chemistry, physics, computer science, and economics. We also have majors who have a second major or minor in areas such as music and English. We offer a Mathematics Secondary Education Minor for students intending to become middle school or high school mathematics teachers. We also offer a Mathematics Elementary Education Minor for students going into elementary teaching.

### Mathematics

A minor in mathematics consists of at least 19 credits from the following courses: MA 126, 131, 132, 231, 232, 280, and all courses numbered above 300 except 323 and 324. No more than 16 credits from courses numbered 232 and lower shall be counted towards the 19 required credits.

Note: For students desiring an applied focus to their minor (e.g., actuarial studies, statistics, mathematical biology, mathematical modeling, etc.) recommended courses include courses in:

- Calculus (MA 126, 131, 132, 231, 232)
- Statistics (MA 311/312)
- Probability (MA 361)
- Linear Algebra (MA 345)
- Differential Equations (MA 370)
- Numerical Analysis (MA 372)

For more specific recommendations for your proposed career, speak with your advisor or a member of the Department of Mathematics.

### Mathematics Elementary Education

In partnership with the Hope College Department of Education, the Department of Mathematics offers a teaching minor at the elementary level for certification through the State of Michigan.

The requirement for a minor in mathematics with elementary teaching emphasis is a plan of study designed in consultation with a departmental advisor, and includes a total of at least 22 credits in mathematics as follows:

- Complete two courses from MA 123, 125, 126, 131, 132 for a total of 8 credits
- Complete MA 205 and 206
- Complete either MA 210, MA 311 and 312, or MA 311 and MA 0110 – Statistics transfer credit
- Complete at least 4 additional credits selected from MA 207, MA 208, and GEMS courses centered on mathematical topics (GEMS 100 or 105).

### Mathematics Secondary Education

In partnership with the Hope College Department of Education, the Department of Mathematics offers a teaching minor in the secondary level for certification through the State of Michigan.

The requirement for a minor in mathematics for those intending to become middle school or high school mathematics teachers is a plan of study designed in consultation with a departmental advisor, and includes a total of at least 24 credits in mathematics as follows:

- MA 132, 231, 280, 311, 312, 321, and 351 must be included
- Additional credits chosen from the following courses: MA 126 or 131, MA 232, and all
courses numbered above 300
*except*323 and 324 - No more than 16 credits from courses numbered 232 and lower shall be counted towards the 24 required credits
- MA 323 and 324 must also be taken (
*this counts as education credit and does not count toward the 24 mathematics credits*)

**Note: a student cannot receive credit for both MA 123 and MA 125, or MA 126 and MA
131.**

## Mathematics

**123. A Study of Functions** — A study of functions including polynomial, rational, exponential, logarithmic, and
trigonometric functions. These will be explored in their symbolic, numerical, and
graphic representations, and connections between each of these representations will
be made. A graphing calculator is required. Cannot receive credit for both Math 123
and Math 125.*4 Credits | Spring | Mathematics II (MA2)*

**125. Calculus with Review I** — This course covers the material typically taught in the first half of a Calculus I
course. The calculus material is supplemented by reviewing topics of high school mathematics
as needed. The calculus topics are also taught at a slower pace. Topics include function
review, limits and continuity, the concept (and definition) of a derivative, and differentiation
rules (product rule, quotient rule, chain rule are included). Cannot receive credit
for both Math 125 and Math 123.*4 Credits | Fall | Mathematics II (MA2)*

**126. Calculus with Review II** — This course is a continuation of Math 125. The topics covered are the topics typically
taught in the second half of a Calculus I course. The calculus material in the course
is supplemented by reviewing topics of high school mathematics as needed. The calculus
topics are also taught at a slower pace. Topics include implicit differentiation,
applications of differentiation, L’Hospital’s rule, Newton’s method, the integral,
and applications of integration. Cannot receive credit for both Math 126 and Math
131.

Prerequisites: Math 125 with grade of C- or better*4 Credits | Spring | Mathematics II (MA2)*

**131. Calculus I** — Topics include functions, limits, continuity, differentiation, integration, and applications
of the derivative and integral. Cannot receive credit for both Math 131 and Math 126.
ACT Math score of 25+ is highly recommended.*4 Credits | Fall, Spring | Mathematics II (MA2)*

**132. Calculus II** — Topics covered include techniques of integration, applications of the integration,
sequences, infinite series, power series, introduction to differential equations,
and polar coordinates.

Prerequisites: Math 126 or Math 131 with a grade of C- or better*4 Credits | Fall, Spring | Mathematics II (MA2)*

**205. Mathematics for Elementary and Middle School Teachers I** — The first of a two-course sequence in which prospective K-8 teachers explore the fundamental
aspects of the mathematics they will be expected to teach in their future classrooms.
Emphasis is on developing a conceptual understanding of the mathematics and the ability
to communicate mathematical concepts effectively to K-8 students. Topics addressed:
Number Concepts and Operations; Algebraic Thinking, Statistics & Probability. Proficiency
in basic mathematical skills is assumed. For prospective elementary and middle school
teachers only. Completion of, or concurrent enrollment in, an Educ 200-level course
is highly recommended prior to this course.

Prerequisites: Educ 220 and Educ 221*4 Credits | Fall | Mathematics II (MA2)*

**206. Mathematics for Elementary and Middle School Teachers II** — A continuation of Math 205 with a focus on geometry and measurement. For prospective
elementary and middle school teachers only.

Prerequisites: Math 205 with a grade of C- of better*2 Credits | Spring | Mathematics II (MA2)*

**207. K-8 Mathematics Software Applications** — A course designed to deepen participants’ understanding of mathematical concepts by
exploring current information and communication technologies used in K-8 classrooms.
As technology rapidly changes, emphasis is on “learning to learn” with different technologies
in a project-focused, collaborative setting.

Prerequisites: Math 205 with a grade of C- or better*2 Credits | Spring, Odd Years*

**208. Problem Solving for Elementary and Middle School Teachers** — A course designed to integrate content areas of mathematics with the practice of problem
solving. Emphasis will be given to group work, oral presentation and multiple solution
methods. For prospective elementary and middle school teachers only.

Prerequisites: Math 205 with a grade of C- or better*2 Credits | Spring, Even Years*

**210. Introductory Statistics** — The course begins by exploring statistical inference for one and two variables using
a randomization approach, while reviewing basic descriptive statistical techniques.
The course then explores the relationship between randomization methods and traditional
inference techniques, estimation using confidence intervals and statistical power
and its impact on sample design decisions. Throughout the course there is an emphasis
on active-learning using group activities and projects, as well as reading and critiquing
research from mainstream and peer-reviewed media sources. Activities, projects and
hands-on learning activities are conducted using a variety of approaches but make
heavy use of the computer and statistical software. Cannot receive credit for both
Math 210 and Math 311.*4 Credits | Fall, Spring | Mathematics II (MA2)*

**231. Multivariable Mathematics I** — The study of linear algebra and ordinary differential equations.

Prerequisites: Math 132 with a grade of C- or better*4 Credits | Fall, Spring | Mathematics II (MA2)*

**232. Multivariable Mathematics II** — The study of systems of differential equations and multivariable calculus including
differention, multiple integration, and calculus on vector fields.

Prerequisites: Math 231 with a grade of C- or better*4 Credits | Fall, Spring | Mathematics II (MA2)*

**280. Bridge to Higher Mathematics: An Introduction to Mathematical Proof** — An introduction to the understanding and creation of rigorous mathematical argument
and proof. Topics include properties of the integers, real numbers, and integers modulo
n. Additional topics may include mathematical induction, elementary set theory, elementary
number theory, recursion formulas, counting techniques, equivalence relations, partitions
and cardinality of sets. There will be a heavy emphasis on writing, in particular
the writing of mathematical arguments and proofs.

Prerequisites: Math 132*3 Credits | Spring*

**295. Studies in Mathematics** — A course offered in response to student interest and need. Covers mathematical topics
not included in regular courses.

Prerequisites: Permission of instructor*1-3 Credits | Fall, Spring*

**311. Statistical Methods** — This course has the same content and learning objectives as Math 210 but the material
is covered in half the time. The course is designed for students who have a significant
prior experience with statistics (e.g., high school statistics course) or calculus.
Read the Math 210 course description for course content details. Cannot receive credit
for both Math 210 and Math 311.

Prerequisites: Math 131*2 Credits | Spring | Mathematics II (MA2)*

**312. Applied Statistical Models** — This course provides a survey of statistical methods students would expect to see
utilized across disciplines in peer reviewed research. As such, the course focuses
on the design and analysis of studies where the research questions involve more than
two variables simultaneously. Topics include multiple and non-linear regression,
non-parametric methods, general linear models, and multivariate statistical models.
The pedagogical approach is similar to that of Math 210 and Math 311.

Prerequisites: Math 210 or Math 311*2 Credits | Spring | Mathematics II (MA2)*

**318. Mathematical Biology** — An exploration of the ways in which mathematics is used to understand and model biological
systems. Using examples from ecology, neuroscience, epidemiology, and molecular evolution,
we will focus on continuous and discrete models and their analytical and computational
solutions. Systems of differential equations, linear algebra, and statistical methods
will figure prominently among the mathematical topics. Students will become familiar
with the statistical, graphical & modeling capabilities of the R computer language.
Cross-listed with Biol 318.*4 Credits | Spring, Odd years*

**321. History of Mathematics** — This course is designed to give mathematics students an opportunity to study the various
periods of mathematical development. Attention will be given to the early Egyptian-Babylonian
period, the geometry of Greek mathematicians, the Hindu and Arabian contribution,
the evolvement of analytical geometry since Descartes, the development of calculus
by Newton and Leibniz, and non-Euclidean geometry. Some attention will be given to
the methods and symbolisms used in problem solving during various periods of time.

Prerequisites: Math 132*2 Credits | Fall*

**323. Teaching of Mathematics in the Secondary School** — Methods of teaching mathematics with emphasis on varied approaches, classroom materials,
curriculum changes, and trends in mathematics education. Cross-listed as Educ 323.

Prerequisites: Declared education major

Corequisites: Math 324*2 Credits | Fall*

**324. Teaching Mathematics in the Secondary School Field Placement** — This is a field placement that must be taken concurrently with Math 323.

Prerequisites: Declared education major

Corequisites: Math 323*1 Credit | Fall*

**331. Real Analysis I** — Study of the real number system, sequences, functions, continuity, uniform continuity,
differentiation, and theory of integration.

Prerequisites: Math 232, Math 280*3 Credits | Fall*

**332. Real Analysis II** — A continuation of Math 331 including functions of several variables, series, uniform
convergence, Fourier Series.

Prerequisites: Math 331*3 Credits | Spring, Even Years*

**334. Complex Analysis** — The study of the algebra and geometry of complex numbers, analytic functions, complex
integration, series, conformal mapping.

Prerequisites: Math 232*3 Credits | Fall, Odd Years*

**341. Algebraic Structures I** — An introduction to algebraic systems including a study of groups, rings, and integral
domains.

Prerequisites: Math 232, Math 280*3 Credits | Fall*

**342. Algebraic Structures II** — A continuation of Math 341 including topics chosen from Galois theory, advanced linear
algebra, group representation theory, and algebraic geometry.

Prerequisites: Math 341*3 Credits | Spring, Odd Years*

**345. Linear Algebra** — The study of abstract vector spaces, matrices and linear transformations, determinants,
canonical forms, the Hamilton-Cayley theorem, inner product spaces.

Prerequisites: Math 231, Math 280*3 Credits | Spring, Even Years*

**351. College Geometry** — A modern approach to geometry for students with some background in calculus and an
interest in secondary teaching. Attention is given to the role of axioms in elementary
geometry and in the development of other geometries.

Prerequisites: Math 280*3 Credits | Fall*

**360. Combinatorics and Graph Theory** — A study of topics in discrete mathematics. Topics may include enumeration, algorithms,
graphy theory, graphy planarity, graph coloring, the pigeonhole principle, permuatations
and combinations, binomial coefficients, search algorithms, generating functions,
and recurrence relations.

Prerequisites: Math 280*3 Credits | Spring, Odd Years*

**361. Introduction to Probability** — This course provides an introduction to both discrete and continuous probability.
Topics include conditional probabilities and independence, combinations and permutations,
Bayes’ theorem, popular discrete and continuous distributions (e.g., binomial, normal,
Poisson, exponential), bivariate and multivariate distributions, covariance and correlation,
moment generating functions and limit theorems. In addition to serving as preparation
for the first actuarial exam, this course also serves as a general introduction to
probability for all students interested in applied mathematics.

Prerequisites: Math 132

Corequisites: Math 363*3 Credits | Fall, Even Years*

**362. Mathematical Statistics** — Emphasis on inferential statistics. Estimation, confidence intervals, testing of statistical
hypotheses, regression and correlation, analysis of variance, control charts, non-parametric
methods.

Prerequisites: Math 361

Corequisites: Math 364*3 Credits | As Needed*

**363. Probability Problem Solving Session** — This course runs concurrent to Math 361 and serves as an opportunity to practice probability
problems. This course is required for all students in Math 361.

Prerequisites: Math 132

Corequisites: Math 361*1 Credit | Fall, Even Years*

**364. Laboratory for Mathematical Statistics** — A computer-based laboratory to aid the learning and understanding of statistical
concepts in Math 362.

Prerequisites: Math 361

Corequisites: Math 362*1 Credit | As needed*

**370. Advanced Differential Equations** — Advanced topics in ordinary differential equations including series solutions and
orthonormal sets of solutions. Introduction to partial differential equations including
the heat equation, the wave equation and the potential equation. Boundary value problems
and Fourier Series will also be covered.

Prerequisites: Math 232*3 Credits | Spring, Odd Years*

**372. Numerical Analysis** — Topics may include the study of the source and analysis of computational error, finding
the solution of an equation, systems of linear equations, interpolation and approximation,
numerical integration and numerical solutions to differential equations.

Prerequisites: Math 232*3 Credits | Spring, Even Years*

**395. Special Studies in Mathematics** — A course offered in response to student and instructor interest. Topics are not generally
covered in the regular course listings. Course may be taken multiple times if topics
are different.*1-4 Credits | As Needed*

**399. Mathematics Seminar** — A course for senior mathematics majors which includes problem solving, student presentations
on mathematical topics, mathematical modelling, and discussions on the history and
philosophy of mathematics. Attendance at department colloquia also required.*2 Credits | As Needed*

**434. Elementary Topology** — A systematic survey of the standard topics of general topology with emphasis on the
space of real numbers. Includes set theory, topological spaces, metric spaces, compactness,
connectedness, and product spaces. Students may take Math 331 either prior to enrollment
in or concurrently with the class.

Prerequisites: Math 331

Corequisites: Math 331*3 Credits | As Needed*

**490. Research in Mathematics** — Course provides opportunity for a junior or senior mathematics major to engage in
a research project in an area of mathematics in which the student has special interest.

Prerequisites: Permission of chairperson*0-4 Credits | Fall, Spring*

**493. Independent Study in Mathematics** — Course provides opportunity for a junior or senior mathematics major to engage in
an independent study project in an area of mathematics in which the student has special
interest.

Prerequisites: Permission of instructor*1-4 Credits | Fall, Spring*

**495. Advanced Studies in Mathematics** — Offered as needed to cover topics not usually included in the other mathematics courses.
A student may enroll for either or both semesters.

Prerequisites: Permission of chairperson*1-3 Credits | Fall, Spring*

**Bekmetjev, Dr. Airat**Mathematics DepartmentVanderWerf Hall-Room 214 27 Graves Place Holland, MI 49423-3617

616.395.7525

bekmetjev@hope.edu**Cinzori, Dr. Aaron**Mathematics DepartmentVanderWerf-Room 216 27 Graves Place Holland, MI 49423-3617

616.395.7528

cinzori@hope.eduMore Information**Doolittle, Stephanie**Mathematics DepartmentComputer Science DepartmentEngineering DepartmentPhysics DepartmentVanderWerf-Room 204 27 Graves Place Holland, MI 49423-3617

616.395.7530

doolittle@hope.eduMore Information**Edwards, Dr. Stephanie**Mathematics DepartmentVanderWerf 218 27 Graves Place Holland, MI 49423-3617

sedwards@hope.edu**Holmes, Dr. Vicki-Lynn**Mathematics DepartmentEducation DepartmentVanZoeren Hall - Room 295A 41 Graves Place Holland, MI 49423-3617

616.395.7714

holmesv@hope.edu**Koh, Dr. Yew-Meng**Mathematics DepartmentVanderWerf 210 27 Graves Place Holland, MI 49423-3698

616.395.7759

koh@hope.edu**Mann, Dr. Eric**Mathematics DepartmentVanderWerf-Room 213 27 Graves Place Holland, MI 49423-3698

616.395.7876

mann@hope.eduMore Information**Pearson, Dr. Mark**Mathematics DepartmentVanderWerf-Room 212 27 Graves Place Holland, MI 49423-3617

616.395.7522

pearson@hope.edu**Pearson, Dr. Paul**Mathematics DepartmentVanderWerf 211 27 Graves Place Holland, MI 49423-3617

616.395.7529

pearsonp@hope.eduMore Information**Stephenson, Dr. Darin**Mathematics DepartmentVanderWerf Hall-Room 219 27 Graves Place Holland, MI 49423-3617

616.395.7524

stephenson@hope.eduMore Information**Stoel, Cathy**Geological and Environmental Science DepartmentComputer Science DepartmentEngineering DepartmentMathematics DepartmentPhysics DepartmentSchaap Science Center 2107 & VanderWerf 204 35 East 12th Street & 27 Graves Place Holland, MI 49423-3605

616.395.7510/7540

stoel@hope.eduMore Information**Swanson, Todd**Mathematics DepartmentVanderWerf 241 27 Graves Place Holland, MI 49423-3617

616.395.7679

swansont@hope.eduMore Information**Vance, Kate**Mathematics DepartmentVanderWerf -Room 209 27 Graves Place Holland, MI 49423-3617

616.395.7721

vance@hope.eduMore Information**VanderStoep, Jill**Mathematics DepartmentVanderWerf 209 27 Graves Place Holland, MI 49423-3617

616.395.7408

vanderstoepj@hope.eduMore Information**Verbrugge, Dawn**Mathematics DepartmentSchaap Science Center 3027 35 East 12th Street Holland, MI 49423-3698

616.395.7530

verbrugge@hope.edu**Yurk, Dr. Brian**Mathematics DepartmentVanderWerf Hall - Room 215 27 Graves Place Holland, MI 49423-3617

616.395.7526

yurk@hope.edu

**Mathematics**

VanderWerf Hall27 Graves PlaceRoom 204Holland, MI 49423

workP. 616-395-7530

cinzori@hope.edu