Mathematics and Statistics
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. Statistics is the study of data. In a world where data is readily available and so many decisions are made from data analytics, students need to be equipped to extract meaning from data.
The Department of Mathematics and Statistics 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 as well as an optional concentration in statistics. 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 offcampus at a variety of domestic locations such as Oak Ridge National Laboratory.
Majors
The Department of Mathematics and Statistics offers both a Bachelor of Science and a Bachelor of Arts in mathematics with the option for a concentration in Statistics. 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.
 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: MATH 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
A Statistics Concentration will include MATH 311, 312, 365 and either Math 313 or 362 as part of the 34 required mathematics 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 and Applied Science division of which at least 39 credits must be in mathematics as follows:
 MATH 280, 331 and 341 must be included
 Additional credits chosen from the following courses: MATH 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
A Statistics Concentration will include MATH 311, 312, 365 and either MATH 313 or 362 as part of the 39 required mathematics credits.
See individual course descriptions for prerequisites.
 Mathematics Secondary Education

In partnership with the Hope College Department of Education, the Department of Mathematics and Statistics 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:
 MATH 132, 231, 280, 311, 312, 321, 331, 341, and 351 must be included
 Additional credits chosen from the following courses: MATH 126 or 131, MATH 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
 MATH 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 and Statistics offers a Minor in Mathematics and a Minor in Statistics for nonmathematics majors. We also offer a Mathematics Secondary Education Minor for students intending to become middle school or high school teachers.
 Mathematics

A minor in mathematics consists of at least 19 credits from the following courses: MATH 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:
 Calculus (MATH 126, 131, 132, 231, 232)
 Statistics (MATH 311/312)
 Probability (MATH 365/366)
 Linear Algebra (MATH 345)
 Differential Equations (MATH 370)
 Numerical Analysis (MATH 372)
For more specific recommendations for your proposed career, speak with your advisor or a member of the Department of Mathematics.
 Mathematics Secondary Education

In partnership with the Hope College Department of Education, the Department of Mathematics and Statistics 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:
 MATH 132, 231, 280, 311, 312, 321, and 351 must be included
 Additional credits chosen from the following courses: MATH 126 or 131, MATH 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
 MATH 323 and 324 must also be taken (this counts as education credit and does not count toward the 24 mathematics credits)
 Statistics

A minor in statistics is available for Nonmathematics majors and consists of at least 19 credits. The following 13 credits are required courses: MATH 132, MATH 311, MATH 312, MATH 365 and one of either MATH 313 or MATH 362.
The remaining 6 credits must be chosen from:
 MATH 131 or MATH 126
 MATH 313 (if not used above)
 MATH 362 (if not used above)
 MATH 366
 MATH 490 Independent Studies (1 cr each) for other Society of Actuaries (SOA) exam preparation
 Programming courses (from Computer Science)
 Data Science courses (from Math/Computer Science)
 other departments' research methods/statistics courses (e.g. COMM 280 Research Methods, PSY 200 Research Methods, ECON 306 Econometrics, SOC 262 Methods of Social Research, KIN 250 Research Methods in Kinesiology)
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)
195. 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
Prerequisites: Permission of Instructor
14 Credits  Fall, Spring
205. Mathematics for Elementary and Middle School Teachers I — The first of a twocourse sequence in which prospective K8 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 K8 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 200level 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)
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 activelearning using group activities and projects, as well as reading and critiquing
research from mainstream and peerreviewed media sources. Activities, projects and
handson 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)
221. Introduction to Mathematics for Elementary Educators — The first in a threecourse sequence in which prospective elementary (PreKindergarten
to 6th Grade) teachers explore the fundamental aspects of the mathematics they will
be expected to teach. Emphasis is on developing a deep conceptual understanding of
the specialized mathematical content knowledge and the methods to communicate mathematical
concepts effectively to children expected of wellprepared beginning teachers. Topics
addressed: How children learn mathematics, Number Concepts, and Properties of Shapes
and Spatial Relationships. Proficiency in basic mathematical skills is assumed. For
prospective elementary and special education teachers only.
Prerequisites: Declared education major
4 Credits  Fall, Spring
223. Mathematics for Elementary Educators — The second course in a threecourse sequence in which prospective elementary teachers
explore the fundamental aspects of the mathematics they will be expected to teach.
Emphasis is on developing a deep conceptual understanding of the specialized mathematical
content knowledge and the methods to communicate mathematical concepts effectively
to children expected of wellprepared beginning teachers. Topics addressed: Mathematical
Development in Children, Additive Reasoning, Multiplicative Reasoning, and Early Fraction
Concepts. For prospective elementary education and special education teachers only.
Prerequisites: Declared education major, Math 221 with a grade of C+ or better
4 Credits  Fall, Spring
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
differentiation, 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
14 Credits  Fall, Spring
308. Mathematical Teaching Practices for Elementary Educators — The final course in a threecourse sequence in which prospective elementary teachers
explore the fundamental aspects of the mathematics they will be expected to teach.
Emphasis is the development of content specific teaching practices, techniques and
dispositions that support sound mathematical teaching. Preservice teachers learn
to value and encourage the development of children’s strategies and invented algorithms
within the context of mathematical operations with fractions. Students will engage
in practicebased explorations of effective teaching and highleverage practices in
mathematics using materials taken from real classrooms. For prospective elementary
teachers only.
Prerequisites: Declared education major, Math 223 with a grade of C+ or better
2 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 or statistics transfer credit
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 nonlinear regression,
nonparametric 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)
313. Statistical Methods III — Recent advances in Data Science have resulted in the introduction of many new methods
in Applied Statistics. This course focuses on the application of some of these new
methods in two of the main branches of Data Science  Prediction (supervised learning)
and Classification (unsupervised learning).
Prerequisites: Math 312
3 Credits  Fall
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.
Crosslisted with Biol 318.
Prerequisites: Biol 105 and Biol 106, Biol 107 or equivalent, Or, Math 231
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 EgyptianBabylonian
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 nonEuclidean 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. Crosslisted as Educ 323.
Prerequisites: Declared education major
Corequisites: Math 324
3 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 HamiltonCayley 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,
graph theory, graph 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
362. Mathematical Statistics — Emphasis on inferential statistics. Estimation, confidence intervals, testing of statistical
hypotheses, regression and correlation, analysis of variance, control charts, nonparametric
methods.
Prerequisites: Math 361 or Math 365
3 Credits  As Needed
364. Laboratory for Mathematical Statistics — A computerbased laboratory to aid the learning and understanding of statistical
concepts in Math 362.
Prerequisites: Math 361 or Math 365
1 Credit  As needed
365. 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, bivariate and multivariate
distributions, covariance and correlation, moment generating functions. This course
serves as a general introduction to probability for all students interested in applied
mathematics.
Prerequisites: Math 132
2 Credits  Fall, Even Years
366. Probability for Actuaries — This course runs in the second half of the fall semester of even years after Math
365 and serves as an opportunity to prepare interested students for the Society of
Actuaries' Probability Exam (Exam P) as well as delve deeper into the Introduction
to Probability course. Students may take Math 365 either prior to enrollment in or
concurrently with the class.
Prerequisites: Math 365
Corequisites: Math 365
2 Credits  Fall, Even Years
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.
14 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
04 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
14 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
13 Credits  Fall, Spring
 Bekmetjev, Dr. AiratMathematics and Statistics Department
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bekmetjev@hope.edu  Cinzori, Dr. AaronMathematics and Statistics Department
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