# Calculus at Western

## Calculus Class Sequences

The Core Math Flowchart on the Math Advising Page shows how the introductory math classes at Western are related to one another and details the relevant class prerequisites.

The information below is intended for those whose first class in mathematics at Western is likely to be a class at the level of calculus. Students who intend to take a class below the level of calculus as their first class in mathematics at Western or who are not eligible to take a calculus class at Western, should consult the relevant advice posted at Courses Below Calculus at Western.

The **standard calculus class** sequences at Western are as follows: there is a two-quarter single variable calculus sequence (**Math 124 – Math 125**), followed by a two quarter multivariable calculus sequence (**Math 224 – Math 225**) and a separate class on series, **Math 226**. For most students, Math 124 is the first calculus class they take at Western. Students who already have college calculus credits from elsewhere or a suitable AP Calculus exam score may be eligible to register for a calculus class beyond Math 124.

There is also an **Honors calculus sequence**, **Math 134 – Math 135**, which parallels Math 124 – Math 125 but is aimed at Honors students and others with high potential. The Accelerated Calculus class **Math 138** is aimed at those who have already established a good grounding in calculus; it reviews some of the key material in Math 124 and Math 125, with a focus on conceptual understanding and applications, in one quarter. Details on the nature of, and admission into, these special classes can be found below.

There is also a one quarter **business calculus** class, **Math 157**, which most students with a business major are required to complete. Students who complete Math 124 are deemed to have completed Math 157. Students intending to major in Economics should consider taking Math 124 instead of Math 157.

## Calculus Class Placement

Placement in beginning math classes is usually based on either the score obtained on the **ALEKS Math Placement Assessment (MPA)**, or on college level math classes completed elsewhere including AP Precalculus or AP Calculus classes. Details on taking the MPA can be found on the MPA page, which also lists the classes for which students are eligible based on their MPA score. For students who have completed college level math classes elsewhere, the Transfer Equivalency Report (TER) details how those classes transfer to Western. That includes any AP, IB or other special credit-bearing classes that students may have completed. A list of the math classes students are eligible to take based on AP Precalculus or AP Calculus exam scores can be found on the Core Math Flowchart on the Math Advising Page. Note that the TER only lists classes completed by the student of which the university has been informed at that point in time; it can take a considerable length of time for transcripts and grades from other institutions to reach and be processed by Western. The TER may thus not be entirely complete and up to date, and it is wise to keep a copy of unofficial transcripts readily available for consultation during class planning and registration.

**For students who do not have any college math credits at the level of precalculus or above or suitable AP exam scores**, the only calculus classes for which they may be eligible are Math 124 or Math 157, and the only way to establish eligibility for these classes is by obtaining a suitable score on the ALEKS Math Placement Assessment (MPA).

**Students who have college credit with a grade of at least C+ for a precalculus class designated PC 1** on the TER are eligible to register for Math 157.

**Students who have college credit with a grade of at least C+ for a precalculus class designated PC 2** on the TER are eligible to register for Math 124. If the grade for that precalculus class was C or lower, then the student is only eligible to register for a class below the level of calculus, or possibly Math 157. In most such cases the student should take the MPA to establish the math classes which they are eligible to take.

**Students with transfer credits for a college precalculus or calculus class** deemed equivalent to a Western precalculus or calculus class are eligible to take the next class in the sequence. Some caution is advisable, especially for students with calculus credit through a College in the High School or a Running Start program, since the transition to the pace and challenge of a Western calculus class can be daunting.

**Students who have completed a three quarter calculus sequence** elsewhere may find that their third quarter calculus class does not transfer as equivalent to any Western calculus class. This is because such classes often consist of some of the material on multivariable calculus covered in our Math 224 class, combined with some of the material on series found in our Math 226 class. While such students will get college credits for that third quarter of calculus taken elsewhere, they may still need to complete Math 224 or Math 226, or both, in order to satisfy the requirements for their major or to meet the prerequisites for some other class. Students will get additional college credits for any such additional math classes they complete. In some cases, individual instructors may accept such a third quarter calculus class in lieu of Math 224 or Math 226 as either a class prerequisite or fulfilling the requirement for the major.

**Students who have completed a four quarter (or three semester) calculus sequence** elsewhere may find that their last calculus class transferred as equivalent to Western’s Math 225, while Math 224 is not listed on their TER. Students with credit for Math 225 are automatically deemed to have completed Math 224 for the purposes of meeting the calculus class requirements for any major at Western, but in this case students do not get any additional credit for Math 224.

**For students who have completed an AP Calculus exam (either the AB or BC version), or passed an IB Math class**, the associated class credit and class eligibility details, along with advice regarding what math class to register for, are provided here or the AP Calculus tables on page 3 of the Core Math Flowchart, found on the Math Advising Page. In general, we recommend that such students be conservative regarding the first calculus class in which they enroll at Western. For most students who scored 3 or higher on one of the AP Calculus exams, one of Math 124, Math 134 or Math 138 is the most appropriate choice. Students who get credit for Math 124 and/or Math 125 by virtue of their AP Calculus exam score will also get credit for Math 134, Math 135 or Math 138 if they complete any of the latter classes, even though there is a substantial overlap in the class contents. These classes focus on a thorough understanding of the underlying concepts and applications, and are also an excellent transition to the pace and level of challenge of college calculus classes. Details regarding the nature of, and admission into, Math 134 and Math 138, and reasons why these classes are a good choice for students with AP credits entering Western, can be found below.

Math 224 is rarely a good choice for students in their first quarter at Western, with the exception of students who have recently completed a sequence of two college calculus classes with really good grades elsewhere, or those with very high scores on the AP Calculus BC exam. Math 226 is an even worse choice for students entering Western, other than transfer students with a strong mathematical foundation.

## Math 134-135 and Math 138: Student Advice

Students can get credit for these classes in addition to getting credit for Math 124 and/or Math 125. This policy is aimed particularly at students who get credit for Math 124/125 via AP exam scores. It is possible to score highly on the AP exams on the basis of computational skills rather than conceptual understanding and the ability to apply those skills, whereas Math 134/135 and Math 138 focus on understanding, modelling, problem solving and applications. Accordingly, many students with Math 124/125 credit via AP scores will benefit significantly, by getting a thorough understanding of the material and the ability to apply it in a variety of settings, from Math 134/135 or Math 138. This credit policy removes any disincentive for students with AP calculus credits to take Math 134/135 or Math 138.

Math 134 and Math 138 are both excellent choices for students with AP calculus credits in their first quarter at Western. These students already have some (possibly superficial) familiarity with much of the material, so they should do well in these classes, which can be really helpful for their confidence as well as boosting their GPA for admission into STEM majors with restricted capacity. These classes do not just reiterate the computational skills these students may already have encountered; instead they focus on understanding and enhance the ability of students to use the tools of calculus in a variety of contexts. These classes also give students an opportunity to revisit some topics from precalculus which are often neglected by high schools in their haste to put students into the more prestigious AP calculus programs.

Even students who might be eligible for Math 125 or Math 224 upon entry into Western would typically be better off taking Math 134 or Math 138 in their first quarter. They are both designed as ‘transition’ (although also challenging) classes, whereas Math 125 and Math 224 are really for continuing students already familiar with the pace and level of challenge of college classes. Moreover, there are topics in the typical college calculus curriculum, including Math 124 and Math 125, that are not in the AP calculus curriculum, so these students are at a disadvantage if starting in those classes. Math 224 in particular is likely to be a disastrous choice for all but the strongest incoming students in their first quarter at Western.

For admission into Math 134, students need to complete and score highly on the MPA, to confirm that their precalculus skills are adequate. They also need to participate in an interview with a Math advisor, who will issue permission to register for the class to suitable students. Invitations to participate in these interviews are sent to potential students identified by means of their high school records or AP calculus results, but interviews can also be arranged by request from other students interested in the program.

Admission to Math 138 is unrestricted to those with suitable AP calculus exam scores, but such students are nevertheless urged to consult with a Math advisor prior to registration to determine the best choice of class for them and to help them to understand the distinctive nature of the Math 138 class.