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Mathematics

Mathematics

FOR INFORMATION contact
Ken Williams, Ph.D.
Liberal Arts Building, Room 327
Direct: (313) 927-1318
E-Mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

PROGRAMS OFFERED
Bachelor of Science, Mathematics Major (B.S.)
Bachelor of Arts, Mathematics Major (B.A.)
Bachelor of Arts, Mathematics Major for Elementary Teaching (B.A.)
Mathematics Minor
Mathematics Minor for Elementary Teaching
Elementary and Secondary Teacher Certification
Elementary and Secondary Mathematics
Endorsement
Pre-engineering Program
    
FACULTY
Jana Abolins, Ph.D.
Charles Brian Crane, Ph.D.
Ken Williams, Ph.D. 

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  • Crane-18 medCharles Brian Crane

    Ph.D., Assistant Professor of Mathematics

    Dr. Charles Brian Crane is a pure mathematician who has been teaching undergraduate mathematics since 2001.

    Brian’s primary research interest is graph theory, a branch of discrete mathematics involving the study of relationships and connections.

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scienceandmath.marygrove.edu

Mathematics Overview

CAREER INFORMATION
The demand for graduates with good mathematical and analytical skills is always strong. Marygrove graduates are currently working as teachers, systems analysts and computer programmers. If you decide to pursue a career or graduate studies after graduation, your mathematical knowledge will be invaluable.

The department of mathematics offers undergraduate courses for students interested in a variety of careers. You might become an elementary or secondary teacher or work with computers. You might pursue a career in the natural or physical sciences, continue with graduate studies or, with additional statistics courses, become an actuary.

POTENTIAL CAREERS
Computer programmer • Systems Analyst • Statistician • Researcher • Engineer • Teacher •  Actuary • Mathematician

GENERAL INFORMATION
The Mathematics Program offers undergraduate courses in mathematics, a Bachelor of Science and a Bachelor of Arts degree with a major in mathematics, a Bachelor of Arts degree with a major in mathematics for elementary teaching, a minor in mathematics, a minor in mathematics for elementary teaching, and elementary and secondary mathematics endorsement programs. You may take courses designed to build basic math skills, as well as calculus, differential equations, discrete mathematics, linear algebra, probability and statistics, and college geometry.

SPECIFIC INFORMATION
The Bachelor of Science or Bachelor of Arts degree with a major in mathematics prepares you to be a problem solver and a part of the answer for tomorrow’s problems. Whether you are interested in solving the problems of the nuclear industry, population growth, natural resources, education or the stock markets, mathematics is an essential element. The Bachelor of Arts degree with a major in mathematics for elementary teaching prepares you to be a leader in mathematics curriculum and mathematics teaching in the elementary schools.

The B.S. mathematics major consists of 34 credit hours in mathematics, and 48 total credit hours in mathematics and science; the B.A. mathematics major consists of 34 credit hours in mathematics; and the mathematics major for elementary teaching consists of 31 credit hours in mathematics. The minor in mathematics will complement any major area of study. A total of 20 credit hours in mathematics is required for a minor. A minor in mathematics will provide you with the knowledge required for advanced study in computer science, economics or any of the natural or physical sciences. The minor is particularly useful as a secondary teaching minor.

The minor in mathematics for elementary teaching requires 23 credits in mathematics and is designed to be an elementary teaching minor.

Students interested in Pre-Engineering should declare a B.S. in Mathematics major and will take a program of study that will prepare students to transfer to Engineering and Engineering Technology programs at other institutions to complete their upper level courses for graduation.

SPECIAL ELEMENTS OF THE PROGRAM
Program Scheduling
The B.S or B.A. in mathematics programs are primarily day programs, although some courses are offered in the evening on a rotating schedule.

Transfer Student Information
The department accepts transfer credits according to the college guidelines. However, major coursework older than 10 years, from time of admittance, will be transferred in as elective credit and may not be applied to the major. Students may petition to the department chair for the older credits to be applied towards the major.

Credit for Prior Learning
Learning derived from life experiences and from individual study is of significant academic value and can often be equated with college-level studies. Students may earn credit by examination, tutorial study and cooperative work experience. Permission of the department chair is required to select these options. Not more than four credit hours in cooperative work experience may be counted within the 120 credit hours required for a degree.

Academic Performance Standard
Only required courses with a grade of C or better can be applied to fulfill the Mathematics  major or minor.

Computer Literacy Requirement
Proficiency in Microsoft Office (Word, Excel, PowerPoint) must be achieved prior to graduation. Students’ computer literacy will be evaluated and assessed through the MTH 325, and the senior seminar course sequence. Writing Intensive Requirement All mathematics majors must take MTH 265 as their writing intensive course.

Senior Seminar Requirement
Students must successfully complete MTH 496A and MTH 496B in order to graduate with a Mathematics Degree (B.A or B.S.). Internship/Cooperative Education It is strongly encouraged that students participate in a summer undergraduate research experience either with a Marygrove College faculty member, or by securing an off-campus internship or fellowship before they graduate. Students may receive elective credit for an internship through MTH 388, MTH 488, and/or MTH 491.

Sigma Zeta National Honor Society
Sigma Zeta is a national science and mathematics honor society. It was founded at Shurtleff College, in Alton, Illinois in 1926. Today, more than sixty local chapters are active in colleges and universities across the United States. The society encourages and fosters achievement of greater knowledge in the fields of science and mathematics. Outstanding scholastic achievement in the fields is recognized through membership in this society.

Awards
Students may be eligible to win the following departmental awards based on their scholarly work and academic performance. The Maria Kostecke Murphy Scholarship is given to a deserving woman majoring in mathematics. The Antoinette Joiner Award is given to an outstanding graduating senior majoring in mathematics.

Bachelor of Science, Mathematics Major (B.S.)

The Bachelor of Science degree with a major in mathematics requires completion of the following components‚ including a minimum of 34 credit hours in mathematics and 48 total credit hours in mathematics and science.

A. General Education Requirements
See GENERAL EDUCATION section of this catalog.

B. Required Mathematics Courses
MTH 251 Calculus I
MTH 252 Calculus II
MTH 254 Calculus III
MTH 265 Discrete Mathematics
MTH 300 College Geometry
MTH 325 Probability and Statistics
MTH 353 Linear Algebra
MTH 371 Differential Equations
MTH 380 Abstract Algebra
MTH 496A Senior Seminar: Library Research
MTH 496B Senior Seminar: Conclusion

C. Related Discipline Requirements
PHY 285 Physics I: Mechanics and Sound
PHY 286 Physics II: Electricity and Light Additional classes in mathematics and/or science to attain the required 48 credit hours in mathematics and science.

D. Non-teacher certification students, with department approval, may substitute MTH 270, Graph Theory, for one of the required courses.

E. Required for Secondary Teacher Certification Students:    
MTH 347 Methods in Teaching Secondary Mathematics

Bachelor of Arts, Mathematics Major (B.A.)

The Bachelor of Arts degree with a major in mathematics requires completion of the following components‚ including a minimum of 34 credit hours in mathematics.

A. General Education Requirements
See GENERAL EDUCATION section of this catalog.

B. Required Mathematics Courses
MTH 251 Calculus I
MTH 252 Calculus II
MTH 254 Calculus III
MTH 265 Discrete Mathematics
MTH 300 College Geometry
MTH 325 Probability and Statistics
MTH 353 Linear Algebra
MTH 371 Differential Equations
MTH 380 Abstract Algebra
MTH 496A Senior Seminar: Library Research
MTH 496B Senior Seminar: Conclusion

C. Non-teacher certification students, with department approval, may substitute MTH 270, Graph Theory, for one of the required courses.

D. Required for Secondary Teacher Certification Students:
MTH 347 Methods in Teaching Secondary Mathematics

Bachelor of Arts, Mathematics Major for Elementary Teaching (B.A.)

The Bachelor of Arts degree with a major in mathematics for elementary teaching requires completion of the following components‚ including a minimum of 31 credit hours in mathematics.

A. General Education Requirements
See GENERAL EDUCATION section of this catalog.

B. Required Mathematics Courses
MTH 110 Elementary Functions
MTH 251 Calculus I
MTH 265 Discrete Mathematics
MTH 300 College Geometry
MTH 310 Concepts in Elementary Mathematics I
MTH 311 Concepts in Elementary Mathematics II
MTH 325 Probability and Statistics
MTH 330 Teaching Probability and Statistics in Grades K-8
MTH 496A Senior Seminar: Library Research
MTH 496B Senior Seminar: Conclusion

C. Non-teacher certification students, with department approval, may substitute MTH 270, Graph Theory, for one of the required courses.

Mathematics Minor

The mathematics minor requires 20 credit hours in mathematics.

A. Required Mathematics Courses
MTH 251 Calculus I
MTH 252 Calculus II
MTH 265 Discrete Mathematics
MTH 300 College Geometry
MTH 325 Probability and Statistics

B. Choose one of the following:
MTH 254 Calculus III
MTH 270 Graph Theory
MTH 353 Linear Algebra (Required for Secondary Teacher Certification Students)
MTH 371 Differential Equations
MTH 380 Abstract Algebra

C. Required for Secondary Teacher Certification Students:
MTH 347 Methods in Teaching Secondary Mathematics

Mathematics Minor for Elementary Teaching

The mathematics minor for elementary teaching requires 23 credits in mathematics.

A. Required Mathematics Courses
MTH 110 Elementary Functions
MTH 300 College Geometry
MTH 310 Concepts in Elementary Mathematics I
MTH 311 Concepts in Elementary Mathematics II
MTH 325 Probability and Statistics
MTH 330 Teaching Probability and Statistics in Grades K-8

B. Choose one of the following:
MTH 251 Calculus I (Required for Elementary Teacher Certification Students)
MTH 265 Discrete Mathematics
MTH 270 Graph Theory

Secondary Mathematics Endorsement

The secondary mathematics endorsement requires 23 credit hours in mathematics and is open only to students currently holding a secondary teaching certificate.

Required Mathematics Courses
MTH 251 Calculus I
MTH 252 Calculus II
MTH 265 Discrete Mathematics
MTH 300 College Geometry
MTH 325 Probability and Statistics
MTH 353 Linear Algebra
MTH 347 Methods for Teaching Secondary Mathematics

Elementary Mathematics Endorsement

The elementary mathematics endorsement requires 24 credits in mathematics and is open only to students currently holding an elementary teaching certificate.

Required Mathematics Courses
MTH 110 Elementary Functions
MTH 251 Calculus I
MTH 300 College Geometry
MTH 310 Concepts in Elementary Mathematics I
MTH 311 Concepts in Elementary Mathematics II
MTH 325 Probability and Statistics
MTH 330 Teaching Probability and Statistics in Grades K-8

Pre-Engineering

Engineers help people and society by creating innovative designs ranging from limb prostheses, joint replacements and heart machines to automobiles, airplanes and computers, to clean water processes, wind turbines and solar panels for alternative energy. Engineers and Engineering Technologists then design and oversee the manufacturing processes to ensure quality products are provided to customers.

The Pre-Engineering program at Marygrove College can be a great stepping stone whether you want to be an architectural, electrical, mechanical, civil or any other engineer. Marygrove’s Pre-Engineering Program has been designed to give you a strong foundation in math, science and basic engineering principles that you can build upon through further and more specialized study. You will be introduced to the engineering professions through internships, field experiences, lectures and guest speakers, and learn about workplace expectations and problem-solving through teamwork.

Students interested in Pre-Engineering should declare a B.S. in Mathematics major and will take a program of study that will prepare students to transfer to Engineering and Engineering Technology programs at other institutions to complete their upper level courses for graduation. Dual diploma programs and integrated Master’s Degree programs are also being developed.

Pre-Engineering Core:
CHM 140 General Chemistry II
ISC 222 Introduction to Engineering
MTH 251 Calculus I
MTH 252 Calculus II
MTH 254 Calculus III
MTH 353 Linear Algebra
MTH 371 Differential Equations
PHY 285 Physics I
PHY 286 Physics II

Additional courses are needed depending on the type of engineering program you choose to pursue. Students must achieve a C or higher in the pre-engineering core courses and maintain a minimum overall GPA of 2.5.

Mathematics Course Descriptions

MTH 099 Pre-Algebra 3 hours
Term: fall, winter, summer; Fee: yes
Basic principles and operations of arithmetic‚ elementary algebra‚ informal geometry‚ systems of measurement, and problem solving techniques to enable students to develop the ability to understand and use basic mathematical methods. Credit in this course does not count toward graduation. Must be completed with at least a C-.

MTH 100 Algebra 3 hours
Prerequisites: MTH 099 with a grade of C- or better, or placement recommendation; Term: fall, winter, summer; Fee: yes
Linear equations and inequalities and their graphs, systems of two equations in two unknowns, quadratic equations, factoring, elementary operations with polynomials‚ rational expressions, exponents and radicals, and word problems. This course may not be used to fulfill general education requirements.

MTH 103 Mathematics for Health Careers 4 hours
Prerequisites: MTH 099 with a C or better; Term: fall, winter
Applies basic mathematical skills in calculations required for the usual dosage determinations, as well as solution preparations using weight, metric, household, and apothecary systems.

MTH 105 Intermediate Algebra 4 hours
Prerequisite: MTH 100 or one year high school algebra; Term: fall, winter, summer.
Real numbers, operations with polynomials and rational expressions, factoring, rational exponents and radicals, first degree equations and inequalities, quadratic equations, systems of equations, logarithms, scientific notation and applications.

MTH 110 Elementary Functions 4 hours
Prerequisites: MTH 105 or two years high school algebra, department approval; Term: fall, winter, summer
Elementary functions, their graphs and applications using a graphing calculator, analytical geometry, polynomial and rational functions, exponential and logarithmic functions, trigonometric functions, trigonometric identities, sequences and series, and the binomial theorem. Designed as a pre-calculus course.

MTH 251 Calculus I 4 hours
Prerequisites: MTH 110 or two years of high school algebra, one year high school geometry, one-half year of trigonometry; Term: fall, winter
Analytic geometry in the plane, functions, limits and continuity, derivatives and applications, and indefinite integrals and applications.

MTH 252 Calculus II 4 hours
Prerequisite: MTH 251; Term: winter
Exponential and logarithmic functions, trigonometric and inverse
trigonometric functions, techniques of integration, indeterminate
forms, improper integrals, Taylor’s formula, and infinite series.

MTH 254 Calculus III 4 hours
Prerequisite: MTH 252; Term: fall, offered alternate years [odd]
Polar coordinates, vectors, vector-valued functions, three dimensional analytic geometry, partial derivatives, and multiple integration.

MTH 265 Discrete Mathematics 3 hours
Prerequisite: MTH 110; Term: fall
Sets, functions, algorithms, mathematical induction, counting methods, permutations and combinations, recurrence relations, Boolean algebra, relations, and matrices. Writing intensive course for math majors.

MTH 270 Graph Theory 3 hours
Prerequisite: MTH 110; Term winter
An introduction to topics and applications of graph theory.
Graph theory topics are selected from the following: paths,
cycles, circuits, Eulerian circuits, Hamiltonian cycles,
generalized pancyclicity, forbidden subgraphs, connectivity,
trees, social networks, planarity, graph colorings, directed
graphs, modeling. Additionally, the course includes an
introduction to set theory, and methods of proof (direct proof,
proof by contradiction, proof by cases, proof by induction).

MTH 300 College Geometry 3 hours
Prerequisite: MTH 110; Term: winter
Properties of geometric figures, proofs, constructions, solving applied problems, use of coordinate geometry and transformation geometry, and Euclidean and non-Euclidean geometry.

MTH 310 Concepts in Elementary Mathematics I 3 hours
Prerequisite: MTH 105; Term: fall
Foundations for learning mathematics, sets, algebraic thinking, numeration, fundamental operations of arithmetic, estimation, number theory, integers, rational numbers, real numbers, and explorations.

MTH 311 Concepts in Elementary Mathematics II 3 hours
Prerequisite: MTH 310; Term: winter
Ratio and proportion, percents, representing and interpreting data, centers and spreads of distributions, concepts related to chance, basic concepts of geometry, congruence, transformations, symmetry and tessellations, similarity, perimeter, area, volume, and explorations.

MTH 325 Probability and Statistics 3 hours
Prerequisite: MTH 110; Term: fall, summer
Sample spaces, probability of events, random variables, counting techniques, descriptive statistics, binomial and normal distributions, confidence intervals, and hypothesis testing.

MTH 330 Teaching Probability and Statistics in Grades K–8 4 hours
Prerequisite: MTH 325; Math Major or Minor for Elementary Teaching; Term: winter, offered alternate years [odd]
Statistical graphs, centers and spreads of distributions, appropriate statistical software and student activities, explorations and investigations, and current issues in mathematics education.

MTH 347 Methods in Teaching Secondary Mathematics 3 hours
Prerequisites: EDU 240, EDU 241, EDU 347, Math major or minor, junior or senior standing; Term: winter
Philosophical basis for mathematics teaching, survey of special programs in mathematics, specific objectives, materials and curriculum planning for mathematics in middle and secondary schools, emphasis on role of problem solving in mathematics teaching. Observations of classroom teaching. Course offered as needed.

MTH 353 Linear Algebra 3 hours
Prerequisite: MTH 251; Term: winter, offered alternative years [even]
Matrices, linear systems, determinants, vector spaces, linear transformations, eigenvalues and eigenvectors, and applications.

MTH 371 Differential Equations 3 hours
Prerequisite: MTH 252; Term: fall, offered alternative years [even]
Differential equations of the first order and first degree, as well as their applications, linear dependence and independence, linear differential equations of order two and higher, series solutions of linear differential equations, and systems of linear differential equations.

MTH 380 Abstract Algebra 3 hours
Prerequisite: MTH 265; Term: winter, offered alternate years [odd]
An introduction to topics and applications of abstract algebra which includes an intensive study of fundamental algebraic structures such as groups, rings, and fields. This course also serves as an introduction to theoretical mathematics and proof writing. Methods of proof utilized will include direct proof, proof by contradiction, proof by induction, and proof by cases. The course is writing-intensive and designed to develop mathematical maturity.

MTH 388 Cooperative Field Experience 1-4 hours
Prerequisites: Departmental approval, junior standing
Supervised work experience in activity related to area of specialization, which is planned in consultation with advisor, co-op supervisor and employer. Recording, reporting, and evaluation of experience will be required.

MTH 491 Independent Study 1-4 hours
Prerequisites: Permission of instructor, mathematics major, junior or senior status; Term: 1, 2
In-depth study of a student-selected topic in consultation with a faculty member.

MTH 496A Senior Seminar: Library Research 2 hours
Prerequisites: Senior standing in the major; completion of general education and writing requirements; completion of preliminary summer library research project; Term: fall
Investigation of a significant mathematical problem with the direction of a faculty member. Use of computer for library informational searches, scientific writing, data analysis and word processing. Oral presentation and paper required. If you intend to take MTH 496A, you must inform the department in the preceding winter semester.

MTH 496B Senior Seminar: Conclusion 2 hours
Prerequisite: MTH 496A; Term: winter
The mathematical problem researched in MTH 496A is brought to a conclusion. An oral presentation and a final research paper are required.