Office of Undergraduate Curriculum, Policy + Records

Undergraduate Academic Affairs

The College of **Arts + Sciences**

**Why is finite 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 finite 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 use 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.

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

**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 class 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.
- 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+ (no max)

**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 40+ (more like 50 in fall due to the curve)
- V 118 recommended placement: ALEKS 35+
- D 116 enforced placement: ALEKS 35-50 and low Math SAT/ACT

**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+

- 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.

Office of Undergraduate Curriculum, Policy + Records

Undergraduate Academic Affairs

The College of **Arts + Sciences**