This guide provides detailed information for math course placement, enrollment, course options and discussion topics for non-Math majors.

## Math placement discussions with students

Enrollment decisions are made by students. Advisors should provide placement advice in the context of not only math placement exam scores, but also the student’s intended major and interests, long term goals, and past experience with math. Most students have options to consider. Students should not seek the “best” or “easiest” placement, but rather the most appropriate for their individual situation. Ideally, students do not view math modeling as a check box, but rather as skill building and as an important contribution to the value and possible outcomes of their undergraduate education.

## Placement

- Math Placement exams
- ALEKS: Adaptive computer based exam that can be taken unprotored at home. Requires a fee. Time spent on the ALEKS may vary depending on student’s strengths and perseverance. ALEKS includes free review modules which are required before each optionally included retake.
- The ALEKS student portal is at: https://mathplacement.indiana.edu/
- Students having technical difficulty with ALEKS may contact ALEKS technical support: https://support.aleks.com/assess_placement
- Continuing students needing access to take or retake the ALEKS should email bestexam@indiana.edu .
- Further information about ALEKS may be found on the math department website: https://math.indiana.edu/undergraduate/aleks-online-math-placement-score.html

- Paper MSA: The math department administers this free 26 question multiple choice exam upon request. It is proctored in person in Rawles 115 during normal business hours. It requires 30 minutes and does not allow a calculator. Direct questions to Ginny Jones (vkjones@indiana.edu)
- ALEKS optional Precalculus and Trig minicourse: self-motivated, independent learners may choose this optional asynchronous online minicourse to review the precalc and trig necessary to prepare for calculus. It requires a fee.

- ALEKS: Adaptive computer based exam that can be taken unprotored at home. Requires a fee. Time spent on the ALEKS may vary depending on student’s strengths and perseverance. ALEKS includes free review modules which are required before each optionally included retake.
- Flow charts
- Placement for Math Modeling
- MATH-J course sequencing
- Text descriptions of the Flow Charts
- Advanced Math course sequencing (not yet available)

Always use webforms on math department website. Ginny Jones typically responds quickly to these webform requests.

**100 level course permissions**- No placement enforced, no perm needed: M 125, X 125, M 127, M 118, V 118, M 119, V 119, M 211
- M 106: Placement enforced. Requires appropriate ALEKS (35), paper MSA score, or prereq. May need permission if using a precalculus prereq, unposted transfer prereq or intercampus prereq.
- D 116: Placement enforced. Requires appropriate ALEKS (40), paper MSA score, or prereq. May need permission if using unposted transfer or intercampus prereq.
- B 110: Placement enforced. Appropriate for Business or Public Affairs majors. Not recommended for College majors.
- J 112: Prereq J 111. Students with appropriate ALEKS score (typically 35) may request permission to start in J 112.
- J 113: Prereq J 112. Students with appropriate ALEKS score (typically 55) may request permission to start in J 113.

**200+ course permissions**- MATH-M 212: Prereq M/S 211. Students with unposted test, transfer work or intercampus prereq may request permission. Students with self reported score on sample Calculus Placement Exam may request permission.
- MATH-M 3xx: Preq M/S 212. Students with unposted test, transfer work or intercampus prereq may request permission.
- MATH-S 211: restriction to Hutton. Motivated enthusiastic students outside of Hutton are welcome to request permission.
- MATH-S 212: prereq S 211. Motivated enthusiastic students with strong calculus 1 background are welcome to request permission.
- MATH-S 303: prereq S 212. Motivated enthusiastic students with very strong single variable calculus background are welcome to request permission. Typically this is a 5 on the AP BC exam, or very strong grades in a regular calculus 2 course.

**Calculus AP exams:**IU grants credit for Math-M 211 for a score of 4 or 5 on the AP AB exam or the BC-AB subscore. Credit for M 212 is granted for a score of 4 or 5 on the AP BC exam. Scores of 3 grant UNDI elective credit.**Precalculus AP exam:**IU grants credit for MATH-M 127 for a score of 4 or 5 on the AP Precalculus exam. This course counts as an elective towards degree hours but is not a math modeling course. This test credit can be used as a prerequisite when requesting permission to add a math modeling course such as D 116 or M 106.**IB exams and CLEP:**IU grants UNDI elective credit for IB Math HL. CLEP credit can be found on the admissions website: https://admissions.indiana.edu/apply/freshman/clep-credit.html.**Calculus Placement exam:**FYE administers a Calculus Placement exam during summer orientation and welcome week in August. This 24-question multiple choice exam is proctored online by Examity and can be taken at home before attending new student orientation. Students may contact the Office of First Year Experience for information about how to sign up for this exam. This exam grants credit for Math-M 211 with a grade of S for Satisfactory. This exam may not be retaken. This exam is not offered during January NSO. A sample exam is available on the math department website. A self reported score on the sample exam may be used to request permission to add M 212, but only the proctored exam grants credit.**Math Exemption exams:**The Math department offers in person proctored exemption exams for MATH-M 211, M 212, M 118 and M 119 during finals week in May and December. Students must sign up in advance in Rawles 115. These exams grant test credit. This type of exam may be retaken in a subsequent semester.

Students may request a faculty evaluation of the content of a math transfer course by submitting the webform on the math department website: https://math.indiana.edu/undergraduate/request-equivalency.html. Faculty require a syllabus including the title of the textbook used and a list of all chapters and topics covered.

## Discussing Transfer and online coursework

- Transfer and online courses provide flexibility
- They are not easier
- They may be shorter in length and faster paced
- They may not provide the same support as in person on campus courses

The minimum grade of C for transfer is higher than on campus.

## Prep courses

- J 111 Intro to College Math: Full semester course covering high school algebra. Good preparation for M 106, D 116-117, or the J 112-113 sequence. Credit counts in degree hours as an elective.
- M 18 Basic Algebra for Finite: Faster paced 8 week review of algebra. Good preparation for M 118 and V 118. Does not grant credit towards any degree requirements.
- M 125 Precalculus: Covers precalculus math in preparation for calculus. Lacks the trig necessary for M 211.
- X 125 Suppl for Precalculus: companion course to M 125, intended to supplement students with weaker algebra preparation. X 125 students must take the associated M 125 class.
- M 126 Trigonometry: covers trigonometry necessary for M 211; also useful for Physics preparation.
- M 127 Precalculus with Trigonometry: Covers both precalculus and trig necessary for M 211.
- ALEKS precalculus and trig minicourse
__:__optional online self paced minicourse for students to review precalc and trig independently. Requires a fee.

## Math Modeling courses

### [See below for more detailed information about math modeling courses]

- M 106 Math of Decision and Beauty: Includes topics related to art (symmetry and perspective) and decision Making (voting, game thy, graph thy). Content does not build
- M 118 Finite Math: half probability and half algebra including applications to business and economics.
- V 118 Finite Math with applications: covers similar material to M 118, in a different order with more calculator use and applications to life sciences
- M 119 Brief Survey of Calculus: applied calculus course with applications to business and economics
- V 119 Applied Brief Survey of Calculus: applied calculus course with life sciences applications
- M 211 Calculus 1: traditional first semester single variable calculus
- B 110 Math for BUS and SPEA majors. Not recommended for College majors.

## Advanced and Honors courses

- S 211 Honors Calculus 1 FALL ONLY: contains material from M 211 plus a gentle introduction to proofs. More abstract and less applied than M 211.
- M 212 Calculus 2 second half of single variable calculus; tends to be more challenging than calc 1
- S 212 Honors calc 2: includes material from M 212 plus a gentle introduction to proofs. More abstract and less applied than M 212.
- See also Areas of Study section for 300 level suggestions

Before making a math placement recommendation or discussing a student’s issues or challenges in math courses, it is best to get a sense of the student’s math background, mindset, and reasons why they may struggle in math. Here are some questions you can start with to get useful feedback and encourage reflection by the student.

- How was your experience taking the ALEKS?
- What was your high school math experience like?
- Do you usually rely on help from tutors, friends and family, or teachers when working on math?
- How do you feel when faced with a problem where you aren’t sure exactly how to start or what the proper steps are to reach a solution?

Here are some points you might find useful when discussing IU’s Math Modelling requirement with students:

- Why is math useful?

“One of the best things about mathematics is that it teaches you to think clearly, no matter what you are thinking about.” – Maria Chudnovsky, Princeton.

“Finite Mathematics may prove more useful to you in everyday life than any other course you take during your Indiana University studies. From analyzing news and political discourse, to understanding life threatening health concerns, to making everyday purchases wisely, to understanding investments, M118 will guide your thinking and help your life. The only limitation to how useful you find this course will be the limitations of your own imagination and creativity.” – Professor Kent Orr, IU.

- Is math at IUB hard?
- It’s new to students: Finite covers topics students may be unfamiliar with from high school
- It requires some algebra: students may not have the right background from high school algebra
- It doesn’t rely on a graphing calculator: students may be accustomed to relying on a graphing calculator in high school
- It requires regular attendance and work: upperclassmen, in particular, may not be in the habit of attending every class and spending an hour or more a night on homework
- It teaches problem solving techniques: students may not be accustomed to the process of assessing problems and discovering the right approach. Disciplined thinking takes effort.

## Additional Resources

- The Student Academic Center has a series of "Success TV" videos in a section of their site titled "How to Do Math" that cover a wide range of useful topics.
- The UD Guides website has a Math Placement section that includes the ALEKS Math Placement chart, exemption exams, and more.
- The Mathematics Department website contains additional information about courses available through their department, academic support + tutoring, an online form through which students can request permission to add a 100-level course, and more.
- The Finite Show

## Math of Decision and Beauty (M106)

The course is designed to appeal to arts and humanities students and will include approaches based on visual modeling of relationships and critical/conceptual reasoning. Each discussion/recitation is kept small (25 students) and meets more often than the typical 3 credit course to allow more of the work to be done during class time. In-class activities will help students develop learning skills in ways applicable beyond this course. The thematic units treated in the course will include the following:

- Graph theory is a relatively new field of mathematics and a foundation for our understanding of modern social and communications networks. The visual nature of the subject will appeal to certain learners, some of whom may struggle with some aspects of symbolic math.
- Voting theory had its origin in revolutionary France, but gained new life with Kenneth Arrow's work around 1950. Arrow's Theorem, a result that shows that there can be no perfect voting system, is important in both Political Science and Economics.
- A Geometry unit will be on the theory of perspective--a major impetus for developments in mathematics during the Renaissance.
- Music studies will include discussion of the relationships between pitches, octaves, and frequencies and the problem of tuning. [Note: Music studies may be omitted by the course coordinator in a particular term]
- Game theory looks at simple two person games that have applications to society, for example the Prisoners' Dilemma.

Note: Unlike finite math, the above topics do not “build.” This means students have natural reset points during the semester if they are struggling or get behind.

Enforced Placement: ALEKS 35+

## Finite (M118, D116-D117, V118)

The topics of this course include basic probability theory, linear algebra, linear optimization, and applications. The applications are mostly in the social sciences, life sciences, and business. This course can be thought of as mathematical literacy for non-mathematicians, enabling them to understand quantitative analyses in many fields. Very useful for anyone who is not in the natural sciences; natural science students should take calculus, and after two semesters of calculus they can take more detailed courses in these topics (specifically, M301 or M303, and M365 or M463). Students with appropriate placement can take D116-D117, which offers the same material at a slower pace. V118 offers variable topics which tend to include many of the same topics as M118, but different applications.

- M 118 recommended placement: ALEKS 50+
- V 118 recommended placement: ALEKS 50+; V 118 instructor also recommends strong reading comprehension.
- D 116 enforced placement: ALEKS 40+

## MATH-M 118 Detailed Course Description

M118 is a course in finite mathematics. It covers different topics than calculus classes do: roughly, calculus studies continuously varying functions and their rates of change. This is very important for students in mathematics, physics, chemistry, or engineering, but in the mid-1950’s professors at Dartmouth University started thinking that students who are majoring in other subjects might find other topics more useful, namely: set theory, probability theory, linear algebra and matrices, linear optimization, Markov chains, and Game Theory. The analysis in the course is mostly of discrete, finite quantities, hence its name. The topics are taught with applications in the social and life sciences and business in mind.

M118 was first offered at IU in Bloomington in the mid-1960’s, and became very popular as a way of learning basic numerical literacy. It became very popular. Following many other business programs, the School of Business started requiring it, and it also began to be taught at other IU campuses.

If one had to describe the purpose of M118 in one sentence, one could do worse than to quote Maria Chudnovsky, a professor at the Program of Applied and Computational Mathematics at Princeton, who said: "One of the best things about mathematics is that it teaches you to think clearly, no matter what you are thinking about." The techniques taught in M118 are not very difficult on their own: they are more like techniques for organizing your thoughts about things. Disciplined thinking takes effort---but so do sit-ups! M118 builds your quantitative thinking muscles. Say you are trying to understand which of several possible situations is true, and are given some additional information. M118 can teach you how to know exactly what the additional information does or doesn't tell you. This is good for understanding medical tests, statistics in the news, financial decisions, and so on.

Say you know that if you have three measurable quantities that satisfy three relations and you fiddle with them for long enough, you can usually figure out what each of them is. M118 teaches you procedures for this kind of thing.

There is a lot of support for students taking M118. The Math Learning Center offers small group tutoring for free on weekdays. There are also Academic Support Centers in three dorms and course-specific Help Sessions in the central campus during evenings. And of course the professors have office hours. Talking through difficulties as they arise is the best way to keep on top of the material.

The ALEKS score predicts fairly reliably whether students have the background it takes to do well in M118. Students who do not have high enough scores can take a slower, two-semester version D116-D117, which is gentler, and still has all the support resources. Students who might want to go in a more mathematical direction in their studies can take M303 and M365 instead of M118, which will cover the topics in more depth (these courses require M211 and M212 as prerequisites; students who might want to go in a more mathematical direction should definitely take those calculus courses as well).

Students who sign up to the appropriate level of the course, show up every time, and do all the work do well in the course. It is hard, but mastering quantitative analysis skills is satisfying as well as being very useful.

## Brief Survey of Calculus (M119, V119)

This is an introductory applied calculus course. Calculus allows us to determine instantaneous rates of change of various quantities that we understand (location of a particle, value of a stock, etc) and, conversely, to take the rate of change of a quantity (velocity of a particle, rate of increase in a stock’s value) and use it to determine the value of the quantity at different times. Along the way, we learn how to calculate areas, volumes, and solve applied problems. V119 covers similar topics to M119, but includes life sciences applications instead of business or economics applications. M/V119 is easier than M211, but it does not count for a math major, and cannot be used as the prerequisite for M212, second semester calculus, and many other useful math courses. (We do offer a one-credit bridge course from

M119 to M212, but it is offered as an emergency measure—it is much easier and better to take M211 if a student plans to go on to M212). Therefore, if a student thinks he or she will need some math for their program or their interests and are not just fulfilling a limited requirement, AND if they have the ALEKS score required, they should take M211. M119 does have a sequel, M120, covering calculus with multiple variables and other topics and applications.

Recommended placement: ALEKS 50+

## Calculus I (M211)

This is the higher-level introductory calculus course. Most natural science majors should take it if they have the ALEKS score required. The course is harder than M119, but the students in it get a better understanding of the ideas in calculus, not just the procedures. This deeper understanding will help them understand on their own how and when to apply the calculus techniques in their work. It is the first in the four-semester calculus sequence which math majors take, and whose second or third courses are prerequisites for most of the more advanced math courses. Students who are unusually good at math can also take the honors version S211 in the fall.

Recommended placement: ALEKS 70+