All students must complete 100 or 200 units (one or two courses) for this requirement through **course registrations or test credit**. The courses that satisfy this requirement present broadly applicable techniques for formulating, analyzing, and solving problems, and for evaluating proposed solutions. Options to complete this section of the core include some Computer Science, Statistics, and Mathematics offerings, including Calculus.

Those who take Calculus must earn credit for the first two quarters of a Calculus sequence (200 units). If you choose to satisfy the requirement with something other than Calculus, you'll take 100 or 200 units of approved non-Calculus coursework. If you complete only 100 units for the Mathematics requirement, you must take an additional 100 units in either the Physical or Biological science categories (for a total of 300 units).

Any student planning to take Calculus should begin the appropriate Calculus course in Autumn quarter of 1st year. Regardless of which Calculus course you test into, you will be able to take it in Autumn. Keep reading to determine if you should take Calculus and, if so, which of those Calculus courses is correct for you.

If you plan to complete the requirement with subjects other than Calculus, you should do so before the end of your 2nd year, but it’s not necessary in your very first term. You should consider it as an option to round out your Autumn schedule. See below to figure out if this applies to you.

The Mathematics Placement test is an online, pre-calculus based test you'll take this summer, regardless of your math plans. It assesses your math background and places you into one of three courses: MATH 11200 Studies in Mathematics I, MATH 13100 Elementary Functions and Calculus I, or MATH 15100 Calculus I. The test must be completed by July 28; see **Placement Tests** page for other logistical details.

Students are exempt from the placement test only if they have AP Calculus scores that place them into MATH 15100 Calculus I or MATH 15200 Calculus II. If you haven't asked College Board to send your scores to UChicago, do so by July 13 to ensure we receive the scores in a timely fashion.

If you performed well in Calculus BC, IB Calculus, or higher-level math at a university or took Calculus but don't have AP scores to apply toward your placement, we recommend that you also take the **Calculus Accreditation Exam**.

Some departments require you to use two quarters of Calculus to satisfy this requirement, including: **all science majors, Economics, Psychology, Public Policy, and others**. Check this by looking at the major’s requirements in the College Catalog; if specific courses are required to satisfy Core requirements, they will be listed under the program’s “Summary of Requirements” under a “General Education” category (example: **Economics**). In some cases the third quarter of the Calculus sequence is required for the major and would then be listed under the "Major" category. The first two quarters of Calculus are also required for **pre-med** **requirements**. See “Determining appropriate placement in Calculus,” below, to figure out which Calculus course is right for you.

If you're certain that you don't want to major in anything that requires Calculus, see "Non-Calculus Options," below.

If you're undecided but there's a chance you might be interested in something that requires Calculus, you should go ahead and take the appropriate Calculus course. The first two quarters of Calculus will satisfy the Mathematics requirement of Core even if you end up in a major that doesn't specify how you are to complete it, so you'll be set either way.

If you plan to take a course for the Mathematics requirement this Autumn, use the information below to consider your options and be prepared to request 2-3 sections of the appropriate course during Pre-Registration.

#### CALCULUS

The Mathematics Department offers three levels of Calculus so that you can take a course appropriate for your background in the subject. For students interested in Honors Calculus, there are two versions available.

A sequence in calculus for students who need some precalculus reinforcement. The sequence completes the necessary background and covers basic calculus in three quarters. This is achieved through three regular one-hour class meetings and two mandatory one-and-one-half-hour tutorial sessions each week. A class is divided into tutorial groups of about eight students each, and these meet with an undergraduate junior tutor for problem solving related to the course. Students completing MATH 13100-13200-13300 have a command of calculus equivalent to that obtained in MATH 15100-15200-15300.

This is the regular calculus sequence in the department. Students entering this sequence are to have mastered appropriate precalculus material and, in many cases, have had some previous experience with calculus in high school or elsewhere. All Autumn Quarter offerings of MATH 15100, 15200, and 15300 begin with a rigorous treatment of limits and limit proofs.

MATH 16100-16200 is an honors version of MATH 15100-15200. A student with a strong background in the problem-solving aspects of one-variable calculus may, by suitable achievement on the Calculus Accreditation Exam, be invited to register for MATH 16100-16200-16300. This sequence emphasizes the theoretical aspects of one-variable analysis and, in particular, the consequences of completeness in the real number system. MATH 16300 also includes an introduction to multivariable calculus.

In this alternate version of Honors Calculus, rather than having lectures from instructors, students are given "scripts" of carefully ordered theorems whose proofs they prepare outside of class and then present in class for comment and discussion. Students interested in an inquiry-based learning (IBL) course should have fluency in spoken English and an AP score of 5 on the BC Calculus exam or placement into MATH 15300.

See "Determining appropriate placement in Calculus," below, to determine which of these sequences is right for you.

Remember that you cannot satisfy the Mathematics requirement of Core with only one quarter of Calculus; you must have credit for both Calculus I and II.

In addition to the Mathematics placement test, the Mathematics department AP Calculus scores and the **Calculus Accreditation Exam** to assess your prior math training. This allows them to identify the most appropriate course for you to take.

A score of 5 on AB Calculus or a score of 4 or 5 on BC Calculus will place you in to MATH 15200 Calculus II, the second course in the year-long 150s sequence. A score of 5 on the BC Calculus exam also garners you an invitation to take MATH 16100 Honors Calculus I or MATH 16110 Honors Calculus I: IBL. This invitation is optional; review the information about Honors Calculus, below, to help you decide if it's right for you.

Note that these **placements are not valid** until we have received your AP Scores from College Board (CEEB #1832). Submit that request to College Board by July 13 to ensure we receive the scores in a timely fashion. Check their website to confirm whether or not you've already asked to have the scores sent.

If you took IB Calculus coursework in high school, you should take the **Calculus Accreditation Exam**.

The **Calculus Accreditation Exam** is always the best route for adjusting your placement level. If you are unsatisfied with your result following this exam, you can speak with the Mathematics department during Orientation Week, but they will want to review with you your results from the accreditation exam. Ultimately, the Math department recommends that you try the course into which you were placed, but you can speak with the Mathematics department at any point during the first few weeks of the quarter if you still feel the course isn’t a good fit. Until then, proceed with the placement determined by the Calculus Accreditation Exam.

Honors Calculus is a highly theoretical course in which students learn to prove all of the theorems of Calculus in addition to seeing many beautiful applications of the subject; the Mathematics department wants you to see the grace and structure of mathematics rather than its mere use as a tool for solving problems. The Mathematics department thinks of these courses as the best possible preparation for further work in higher mathematics, regardless of your intended major.

Honors Calculus is a great introduction to the discipline if you’re interested in further study, but it is not a prerequisite to success in the Mathematics major or other quantitative programs. Consider what unique things you'd get out of the Honors experience and decide whether the time invested would be worthwhile to you based on your future plans.

Keep in mind, if you choose to take Honors Calculus, you forgo credit for whatever portion of the Math 150s sequence that you earned through the AP Exam or the Calculus Accreditation Exam.

Both versions of Honors Calculus, MATH 16100-16200-16300 and MATH 16110-16210-16310, are serious theoretical treatments of univariable (and some multivariable) Calculus for students without previous exposure to theoretical mathematics. In both versions of the course, students learn the rigorous underpinnings of Calculus.

The former is a more traditional course with lectures, homework assignments, and exams, taught from the text Calculus by Michael Spivak. The latter is an Inquiry-Based Learning (IBL) version of the course. In such a course, students are given "scripts" of carefully ordered theorems whose proofs they prepare outside of class and then present in class for comment and discussion. The instructors do not lecture, and in fact, only contribute by choosing the student presenters and commenting after fellow students have had a full chance for questions and comments. After in-class presentations and discussions, students write up polished proofs in "journals" which are submitted for grading. Students selecting this version of the course should be fluent in spoken English and should be prepared to present their arguments for public discussion.

The following majors require Calculus III: Biochemistry, Chemistry, Economics, Mathematics, Physics (in some cases), and Statistics. Others have MATH 15300 as an option for a requirement in the major. Check your major’s requirements in the **College Catalog**; if Calculus III is required or optional for the program, it will be listed under the program’s “Summary of Requirements” under the “Major” category. MATH 15300 is offered every quarter.

This exam is designed to correlate with coursework offered at Chicago, and we put great stock in its ability to find the most accurate mathematics placement for our students. It is only available in the summer prior to matriculation.

The Calculus Accreditation Exam is recommended for those who performed well in Calculus BC, IB Calculus, or higher-level math at a university and anyone who took Calculus but doesn’t have AP scores to apply toward their placement.

This is a written exam that covers all the theoretical and practical aspects of univariable Calculus, plus elements of multivariable Calculus such as partial derivatives and multiple integrals.

It is the only way to raise your original placement as set by the Mathematics Placement Test (MATH 11300, 13100, or 15100) or AP Calculus scores (MATH 15100 or MATH 15200 with an invitation to MATH 16100). Depending on your background, it can even place you beyond Calculus.

Depending on your background, you can be placed into one of the following:

- MATH 13100 Elementary Functions and Calculus I
- MATH 15100 Calculus I
- MATH 15200 Calculus II
- MATH 15300 Calculus III
- MATH 15910 Introduction to Proofs in Algebra OR MATH 19520 Mathematical Methods for Social Sciences OR MATH 20000 Mathematical Methods for Physical Sciences I
- MATH 20300 Analysis in Rn-1 OR MATH 20250 Abstract Linear Algebra

It's also possible tor receive an invitation to take one of the following Honors courses:

- MATH 16100 Honors Calculus I/MATH 16110 Honors Calculus: IBL I
- MATH 20700 Honors Analysis I

Your placement will never be lowered by taking the exam; the final result will be whichever is higher between the exam and your original placement.

Yes, it does. So if someone places into MATH 15200 Calculus II, for example, they can start in MATH 15200 and earn credit for MATH 15100. However, if you place into MATH 15200 with an invitation to take the Honors Calculus sequence and opt to take MATH 16100 Honors Calculus I, you will forfeit the Calculus I credit earned via exam.

The **Calculus Accreditation Exam** can place students into the higher-level courses. If you test into and complete one of these courses, you will also earn credit for Calculus (MATH 15100-15200-15300). Possible outcomes are listed above.

It is administered in numerous locations in the United States and abroad, and there are options for you to independently arrange a proctor to oversee your exam. For all logistical details, including deadlines, see **Calculus Accreditation Exam **page.

First of all, remember you're required to take the online **Mathematics Placement Test** this summer, even if you don't currently expect to take Calculus (note: certain AP Calculus scores can substitute for the online placement test).

If your major doesn’t specify how you are to satisfy this requirement, you have the option of using 1) two Calculus courses at the appropriate level (earned via enrollment or exam), 2) one or two approved non-Calculus courses, or 3) credit received for a 5 on the AP Statistics exam.

More information about non-Calculus options can be found below. Remember: if you take only one non-Calculus course for the Mathematics requirement, you will need to take an additional Core course in either the Physical or Biological sciences.

The courses listed below are approved to satisfy the Mathematics requirement as an alternative to Calculus. These are the eligible courses offered this Autumn quarter; see the **College Catalog** for the complete list.

Remember that you may not combine one of these courses with one quarter of Calculus to complete the Mathematics requirement of Core.

MATH 11200 AND MATH 11300 (Studies in Mathematics II) cover the basic conceptual foundations of mathematics by examining the ideas of number and symmetry. MATH 11200 addresses number theory, including a study of the rules of arithmetic, integral domains, primes and divisibility, congruences, and modular arithmetic. While students may take MATH 11300 without having taken MATH 11200, it is recommended that MATH 11200 be taken first. These courses are at the level of difficulty of the MATH 13100-13200-13300 calculus sequence.

This course introduces statistical concepts and methods for the collection, presentation, analysis, and interpretation of data. Elements of sampling, simple techniques for analysis of means, proportions, and linear association are used to illustrate both effective and fallacious uses of statistics.

This course covers principles and techniques for the analysis of experimental data and the planning of the statistical aspects of experiments. Topics include linear models; analysis of variance; randomization, blocking, and factorial designs; confounding; and incorporation of covariate information.

This sequence, which is recommended for all students planning to take more advanced courses in Computer Science, introduces the discipline mostly through the study of programming in functional (Scheme) and imperative (C) programming languages. Topics include program design, control and data abstraction, recursion and induction, higher-order programming, types and polymorphism, time and space analysis, memory management, and data structures including lists, trees, and graphs. NOTE: Non-majors may use either course in this sequence to meet the general education requirement in the mathematical sciences; students who are majoring in Computer Science must use either CMSC 15100-15200 or 16100-16200 to meet requirements for the major.

Programming in a functional language (currently Haskell), including higher-order functions, type definition, algebraic data types, modules, parsing, I/O, and monads. Basic data structures, including lists, binary search trees, and tree balancing. Basic mathematics for reasoning about programs, including induction, inductive definition, propositional logic, and proofs.