Department of Mathematics

Preparing For Mathematics at MSU

Entrance Requirements

Each student entering Michigan State University must satisfy the University minimum entrance requirement of three years of college preparatory mathematics consisting of two years of algebra and one year of geometry.

While the entrance requirement is for three years of mathematics, students who have taken ONLY three years of high school mathematics place themselves at a severe disadvantage, as most students who enter MSU with the very minimum amount of mathematics find that they are placed into remedial mathematics and must take an extra math course at MSU to satisfy the graduation requirements (see the next section). This situation tends to increase both the time and the cost needed to complete a degree program. For this reason, students are STRONGLY encouraged to take at least FOUR years of high school mathematics, including a course which is designed as a preparation for Calculus.

Graduation Requirements

To graduate from Michigan State University, a student must meet the University Mathematics Requirement by satisfying one of the following (click course titles for descriptions and prerequisites):

  1. Take one course from among MTH 110 or MTH 116.
  2. Take two courses: MTH 103 (see note below) AND one of the following:
    MTH 112, MTH 114, MTH 124, MTH132, MTH152H, MTH 201, STT 200, STT 201.
  3. Take MTH 101 AND MTH 102.
  4. Take MTH 103 AND (MTH 101 OR MTH 102).
  5. Take the proctored mathematics placement exam and obtain a score of 19 or higher.


A MTH 103 waiver can be obtained by receiving a 15 or higher on the mathematics placement exam.

Students who are not adequately prepared mathematically to be successful in MTH 101, MTH 102, or MTH 103 may need to take the remedial course MTH 1825 before taking MTH 101, 102, or 103.

College and Departmental Requirements

In addition to the University requirements, many of the colleges in the University have mathematics requirements associated with particular degree programs. Further, many departments within the colleges require specific mathematics courses, and some limited enrollment programs require a minimum grade-point-average over a collection of courses that include some specific mathematics courses. Please check with your college or department to find out their specific mathematics requirements.

Placement into Mathematics Courses

All entering freshmen and some transfer students (depending on the math credit they are transferring to MSU) are required to take the Mathematics Placement Service Exam (MPS Exam) before attending their Academic Orientation Program (AOP) with the following exceptions:

  1. Students with credit in at least one of the following: MTH 103, MTH 110, MTH 116, MTH 124, MTH 132, MTH 133, MTH 234 or any math course above MTH 234 need not take the MPS exam.
    NOTE: However, students who transfer one of the following: MTH 112, MTH 114, MTH 201, STT 200 or STT 201 alone, with no other math course above the level of MTH 1825, must take the MPS exam (on-line prior to AOP or at AOP). or...
  2. Students who have received Advanced Placement credit for calculus prior to the AOP, or
  3. Students who have either an ACT Math score of at least 28 or an SAT math score of at least 660 and who will also be taking math courses at MSU.

Students who have statistics course credit, but do not fit into any of these three categories should take the Math Placement Exam.

The actual MPS Exam together with a great deal of additional detailed documentation, an FAQ, and other services (including a sample exam and a diagnostic exam) related to the exam are available from the Math Placement Service web site.

Students who have been admitted to Michigan State University may take the exam from this web site, and the result will be recognized for all purposes EXCEPT to satisfy the University mathematics graduation requirement. To satisfy this requirement by a high score on the placement exam, a student must take the test in a proctored setting.

Students who are required to take the Math Placement Exam but do not take it prior to AOP are required to take the placement exam at their AOP. It should be noted that this often occurs in mid to late summer, when students have been away from mathematics for a while.

There are two obvious advantages to taking the placement exam prior to the orientation session. (1) A student who is not satisfied with his/her placement has time to do something about improving the score on the exam, either by extra study or by taking an additional mathematics course either during the school year or the summer. (2) The time at orientation normally allotted to testing can be used for other purposes.

Here is how placement exam scores are interpreted:

Score Recommended placement
0-9 MTH 1825
10 or higher MTH 101, MTH 102, MTH 103 or MTH 110
12 or higher MTH 116
15 or higher MTH 112, MTH 124, MTH 201, STT 200, or STT 201
19 or higher MTH 132

Of course, a student may enroll in a course which requires a lower placement score than the score actually achieved. In general, students at the low end of the range for a particular course may be well advised to consider registering for a course which requires a lesser score.

A student's score on the mathematics placement exam is intended to warn a student away from a course that is well beyond his/her present capabilities. Historical data kept by the math department has shown that if a student attempts a course higher than the placement score indicates is appropriate, then a low grade and quite possibly a failing grade is a VERY LIKELY OUTCOME. This experience has caused the department to require that students register only for the courses recommended for their placement score, regardless of a student's high school record.

Further details about the placement exam may be obtained directly from the Math Placement Service web site.

Placement and Credit for Advanced Placement Calculus

Some high school students have the opportunity to take Advanced Placement Calculus (either the AB or BC version), and these students may qualify for credit for some beginning calculus courses at MSU, provided that they demonstrate an adequate level of achievement in the Advanced Placement (AP) exam. Also, students who do well on the AP Calculus exam in high school are candidates for courses in the honors calculus sequence (MTH 152H, 153H, 254H, and 255H).


  1. Calculus AB test score x = 4, 5, eligible for MTH 132 credit (Calculus I); x = 1, 2, 3 no credit.
  2. Calculus BC test score x = 3, 4, 5, eligible for MTH 132 and MTH 133 credit (Calculus I and II); x = 1, 2, no credit for either MTH 132 or MTH 133.

Observations on Placement and Overall Success

Each fall, approximately 30 per cent of incoming freshmen place into Math 1825, approximately 30 per cent place into Math 103, approximately 20 per cent place into Math 116, and approximately 20 per cent place into Math 132. Extensive surveys are taken on incoming students relative to previous mathematics and current placement. Because so many students place into remedial mathematics, the information these surveys give relative to placement into Math 1825 might be of interest. All of the following seem to be necessary, but not sufficient, in order for an incoming freshman to place OUT OF remedial mathematics (Math 1825, Intermediate Algebra):

  • (a) 4 years of college preparatory mathematics in grades 9 through 12,
  • (b) an average of B or better in high school mathematics courses, and
  • (c) an ACT score of at least 19 in mathematics

The following have also been established by various studies:

  1. More than half the students entering MSU who have had less than four years of mathematics in high school place into remedial mathematics (Math 1825).
  2. About one in five students who place into remedial mathematics (Math 1825) fail the course. Many of these do not finish a university degree within six years.
  3. More than half of the students who place into remedial mathematics had a B average or better in high school mathematics.

From all of this, it should be clear that enrollment in high school mathematics courses, per se, does not provide sufficient background for students who will attend Michigan State University. Mastery of the material is essential. It is important that students learn mathematics with an emphasis on understanding and applications AS WELL AS routine manipulative skills.

Prerequisite Knowledge for Selected 100-level Courses

Here is a very brief description of what students should know before entering some of the 100-level courses at MSU.

Students entering MTH 101 (Quantitative Literacy I) AND MTH 102 (Quantitative Literacy II) should have a foundation in Intermediate Algebra. The goal of these courses is to show how mathematical concepts apply to contextual situations in various areas of society. Upon completion of either of these courses, students would have the option of completing STT 200 if necessary for their major degree. However, completion of these two courses assumes no further mathematics courses will be taken. Completion of both of these courses satisfies the university graduation requirement.

Students entering MTH 103 (College Algebra) should be able to:

  • Plot points in the Cartesian plane.
  • Solve linear equations and inequalities in one variable.
  • Write equivalent algebraic expressions involving polynomials, radical, exponents, and fractions.
  • Interpret points on the graph of a relation in the plane as solutions to an equation in (possibly) 2 variables.
  • Translate English phrases and sentences into mathematical expressions and equations/inequalities, especially those describing how one quantity depends on another.
  • Sketching the graph of a linear equation in two variables is covered in this course.

MTH 116 (College Algebra and Trigonometry) is a 5 credit course and covers material similar to that in Mathematics 103 and 114, but moves at a much quicker pace, and it is expected that students enrolling in Mathematics 116 will have a considerably stronger mathematics background than those enrolling in Mathematics 103 . Mathematics 116 is one of the courses that satisfy the university mathematics graduation requirements. Students cannot receive credit in both MTH 103 and MTH 116.

Students enrolling in MTH 112 (The Significance of Mathematics) should have the same understanding of algebra as students entering MTH 124. MTH 106 is intended for non-science and non-technical students and covers a variety of mathematical topics. It is one of the courses that satisfies the university graduation requirement.

Students entering MTH 110 (Finite Mathematics and Elements of College Algebra) should have good arithmetic skills, particularly in handling fractions. Also, they should be able to do all the things expected of students entering MTH 103. MTH 110 is a 5 credit course covering finite mathematics and some parts of college algebra). MTH 110 is one of the courses that satisfies the university mathematics graduation requirements.

Math 114 (Trigonometry) is a bridge course, designed to prepare a student who has completed MTH 103 or MTH 110 for entry into Calculus (MTH 132), by providing the necessary knowledge of trigonometry. A student entering this course should have the same background as is needed for success in MTH 124. MTH 114, coupled with MTH 103, will satisfy the University mathematics requirement for graduation.

MTH 124 (Survey of Calculus I) is a course intended for those who need to be familiar with the concepts of calculus, but are not likely to use calculus in great depth. Students entering MTH 124 should have a good understanding of algebra, especially the concept of function, including graphs of functions, compositions, and inverses. In this context, students should be familiar with several fundamental examples of functions, such as polynomials, rational functions, exponential functions, and logarithmic functions. In addition, students should have the related manipulative skills. MTH 124 is one of the courses that satisfies the university mathematics graduation requirements.

MTH 132 (Calculus I) is a first "technical" course in Calculus. It is intended for those who will make serious use of calculus in their major area. A student entering MTH 132 should have a HIGHLY DEVELOPED understanding of algebra, a SOLID knowledge of trigonometry, and the related manipulative skills. Although MTH 132 is one of the courses that satisfies the university mathematics graduation requirements, it is expected that students taking MTH 132 will continue with MTH 133, and possibly additional mathematics.

It should be noted that many of the freshman level mathematics courses at Michigan State University require the use of a graphing calculator. Currently, the model recommended is the TI 84+. Other models may be acceptable if they have the following features:

  • a. ability to graph several functions simultaneously,
  • b. trigonometric functions,
  • c. matrix computations, and
  • d. statistics capabilities.

Of course, the exact capabilities needed will vary from course to course. Graphing calculators which may have been used in connection with high school courses are often appropriate for many of MSU's courses, but individual students should check with the course instructor to be sure.

Careers In Mathematics

Several years ago, a national poll was conducted to find the most satisfying profession. Among the factors considered were salary, job stress, and working conditions. The highest ranking went to the actuarial profession. Actuaries work for insurance companies and other financial institutions, and are involved in long term financial planning. Most actuaries have an undergraduate major in mathematics, and a knowledge of calculus and statistics is essential for entry into this profession. The Mathematics Department offers a major in Actuarial Science as well as a minor (which can be taken with any major the university offers).

While many mathematics majors go on to teach at various levels, several recent graduates of Michigan State University with mathematics majors have gone to medical school and to law school. In addition, there are jobs for mathematicians in research and development, computer-related industries, and business. The Social Security Administration, the Environmental Protection Agency, and the National Security Agency all employ large numbers of mathematicians, as do many other branches of federal and state governments.

Michigan State University has one of the largest university student placement services in the nation. According to a recent national survey, students with a bachelor's degree in mathematics had an average starting salary which was higher than all except those with majors in engineering, physics, chemistry, and nursing, and was substantially higher than all majors outside the field of science.

Here are a list of some companies and the jobs for which they have interviewed mathematics majors at Michigan State University: Hewitt Associates - administration consultant; National Security Agency - mathematician; Nippon Motorola Ltd. - design and development engineer; State Farm Insurance - programmer/analyst; Arthur Anderson Co. - financial management consultant; MIT Lincoln Laboratories - research and development; David Taylor Research Center - research scientist; Center for Naval Analysis - operations research; Allstate Insurance - actuarial work; Microsoft Corporation - systems engineer; Doeren Mayhew & Co. - systems engineer; Assured Investment Planners - management trainee; Square D Company - inventory analyst; Auto Owners Insurance - actuarial analyst; Accident Fund Insurance - actuarial analyst.

Many students with strong aptitude in mathematics, after completing their degree, might do well to consider further study. In the field of mathematics, students with above average ability can almost always receive financial support for masters degree and Ph. D. study in the form of an assistantship, and most students find that the compensation from an assistantship is adequate to pay tuition and living expenses while studying for an advanced degree. Nationally, almost all U. S. citizens who are graduate students in mathematics receive "full expense" financial support in the form of an assistantship.

Those who might like further information about what persons with extensive mathematical training actually do besides teaching, might want to look regularly at the web page located at

By clicking on "Career Information", and following the various prompts, one has access to a number of profiles of persons whose academic training is mostly mathematical and who currently work in industry. These articles describe both the training of the person involved and the nature of the functions he/she now performs. These articles change monthly.

Diagnostic Exam

The Diagnostic Exam is a collection of exercises from Algebra I, Algebra II, and Precalculus. The exam was created by a committee consisting of members of MSU Mathematics Department, MSU Division of Science and Math Education, and local high school math teachers (for complete list see Acknowledgements). The goal of this exam is to ensure that students possess certain basic skills so that they are prepared for college level mathematics.

The exam consists of six 20 question blocks. The online solutions provide (in most cases) step by step solutions to each question. Each solution also contains a classification (title) which should reference topics from most (if not all) high school textbooks. In many cases, the solutions include references to other helpful (requisite) problems as well as suggestions on specific topics to review.

Students are encouraged to take the test in the appropriate blocks (see link) under exam conditions (i.e. pencil, paper, calculator). Although there is no grade assigned, students should be able to answer 18+ questions correctly in each block to consider themselves proficient in the area tested.

Warning: This does not guarantee success at the university level but the exam should serve to guide students in proper direction.

Finally, students are encouraged to take this exam as soon as it becomes practical during the corresponding high school course (for instance, it would be impractical to take the Precalculus II block before learning any trigonometry) and perhaps once again as the course comes to completion.

Diagnostic Exam

Diagnostic Exam Solutions