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Mathematics is at the heart of many different sciences and at the gateway of many different disciplines. It is the language used to express laws of nature and many phenomena in various subjects, including medicine, psychology, sociology, biology, economics, computer science, engineering, and more.

Several Mathematics courses fulfill the School of Arts and Sciences Formal Reasoning and Analysis Requirement.

Incoming first year students should take the online Canvas Math Diagnostic Placement Exam during the advance registration period. The results of this will be discussed with your advisor and the exam score will be used, in conjunction with a student's math experience and standardized test scores, to determine the appropriate placement in a Math course. All other students (transfer, exchange and students taking Math beyond the first year for the first time) should consult with their academic advisor before selecting a Math course.

The basic Math Sequence is the Calculus Sequence and two semesters in Algebra and Analysis. In addition, the Math 1610 course begins the honors calculus sequence aimed at students who are interested in Mathematics, but not necessarily Math Majors.

Our ADVANCED COURSES are designed mostly for math majors, however, these courses are also popular with Economics, Physics, and Statistics Majors, as well as students in SEAS and Wharton. The overall goal of these courses is to provide the students with a thorough mathematical education that will prepare them either for graduate school and a research career or for a variety of opportunities in business and industries where high level mathematics can be applied.

On This Page
1. Advanced Placement and Transfer Credit
2. Description of courses:   First yearSecond year
3. Which course should I take?
4. Permit to enroll in a closed or evening course
5. Change to a more elementary calculus Course
6. Computers
7. Honors Calculus

Pause?  For most people it is unwise to take a semester off between math (or language) courses. Rust sets in and can be difficult to remove.

Advanced Placement (AP) and Transfer Credit

It is our policy to waive prerequisite course requirements for those students who can pass an examination that demonstrates that they know the material. These remarks apply especially to the first-year calculus courses. For these, a student may receive credit towards the degree (in addition to the waiving of prerequisites) by either of the methods listed below:

1. For students entering in 2025 and later, passing the external College Board Calculus BC Exam with a score of 5 gives credit for Math 1300 and waives the Math 1400 prerequisite (students entering in 2024 and before receive credit for Math 1400). Lower scores on the BC Exam receive no course credit. No credit is given for the AB Exam. For students entering in 2024 and later, passing the IB Analysis & Approaches HL exam waives the 1400 prerequisite but is not awarded credits. First year students who wish to take Math at Penn should take the Canvas Math Diagnostic Placement Exam regardless of whether they have received AP credit.

2. Passing the Credit by Exam administered in the first or second week of the fall and spring semesters by the Mathematics department. A student in their first, second, or third semester at Penn may take the examination regardless of whether he or she took the external exam described under (1) above. The department does not post records of those who fail the exam.  

Near the end of the summer, the times and dates of the departmental credit by exams will be posted here. The exams are open to all without charge. Students can take credit by exams for Math 1070, Math 1080, Math 1300, Math 1400, Math 1410, Math 2400 and Math 2410.

Students will find the syllabus, core homework problems, practice exams and old final exams for each of the calculus courses posted on the course links above.

NOTE:  You will need to bring identification and a #2 pencil to the exam. No calculators are allowed, but some courses permit students to bring in one page of notes.  The note page should be no larger than 8.5 × 11 inches; it may be handwritten or printed on both sides.  Your notes will also be collected with your exam paper.

You can take more than one exam. For example, if you pass the first exam in Math 1400, you could take Math 1410 in the next exam. Your second exam will not be graded unless you passed the first. The exams must be taken sequentially, if you plan to take a second exam.

3. Retroactive Credit: The Mathematics Department is phasing out retroactive credit. Students in the Class of 2028 and beyond will not be eligible for retroactive credit. Students in the Class of 2027 or Class of 2026 are eligible under the conditions below to receive retroactive credit for Math 1400 (only) by obtaining a grade of B or better in Math 1410, Math 2400, or Math 2600 at Penn. Students in the Class of 2025 or 2024 are additionally eligible to receive a credit for one (and only one) of Math 1400, Math 1410, or Math 2400 upon completing Math 2410 with a grade of B or better. Students must email to request retroactive credit (include your Penn ID#). Retroactive credit will be given based on any grade of  " B" or better. Special COVID Policy:  Any "Pass" grade for courses completed in Spring 2020, Fall 2020 and Spring 2021 also allows for retroactive credit. Students cannot receive retroactive credit by passing our credit exam exam, nor can students receive retroactive credit from transfer credit. Retroactive credit is only given for calculus courses taken at Penn.  Processing of Retroactive credits will end on Dec 10th in the Fall and April 10th in the Spring.

4. Transfer Credit: To be eligible, you must have taken a calculus course during the regular academic year (Fall or Spring semester) at another College or University and receive a grade of C+ or better (Math 1300) or C or better for any other Calculus course. Instructions for submitting requests for transfer credit are here.

Important Note: We do not give credit for any course taken during high school, or for any course given at or by a College or University which is specifically designed for high-school students. We do not give transfer credit for Calculus courses taken at other Colleges or Universities during the summer, nor do we give transfer credit for Calculus courses taken elsewhere over the web (even if they are taken during the regular academic year). Taking such courses, however, may well be useful in preparing for the Departmental Credit by Exam (see above).

No credit can be awarded for Math 101-type courses (i.e., any precalculus course) under any circumstances.

Dropping AP credit: Students are not always prepared for all the AP credit they receive. Therefore, students are permitted to drop one unit of AP credit. To do this, come to the Math office DRL 4W1 and sign a petition before the end of the ADD period in September. Or, send an email to with your PID#

Description of Courses

First-year courses

During the advance registration period over the summer, incoming first year students will take the online Canvas Math Diagnostic Placement Exam. Your academic advisor will take into account the results of this exam when helping you select the appropriate Math course.

Math 1300, Introduction to Calculus, as its title signifies, provides an introduction to Calculus for students who have not had exposure to or passed AB Calculus or who needs further practice.

Math 1400, Calculus , the first calculus course, assumes that students have had the equivalent of AB Calculus in high school, and are familiar with calculus concepts through applications of differentiation and basic integration techniques.

Decline Advanced Placement Credit?  
It is sometimes tempting to decline Advanced Placement Credit and take the course again for an "easy A". In practice this can backfire since you don't study and, at the end of the semester know less than at the beginning. Upshot: boredom and a lower grade.
Thus, be careful before declining AP Credit (see also Changing Calculus Courses).

There are two second-semester Calculus courses. Students are advised to check their major department or their program for the specific requirement. In general, Math 1410, Multivariable Calculus is taken by students in the natural sciences, engineering and economics. Math 1410 prepares students for the more advanced Calculus courses Math 2400 and 2410. Those who do not plan to take Math 2400 may still want to consider taking Math 1410. Wharton students can take Math 1410 or Math 110.

Math 1610 is an Honors version of Math 1410 and explores the mathematical underpinnings of the subject matter in greater depth than the standard 1410 class.

Math 1700 Ideas in Mathematics.This course is intended for students who, without getting too technical, would like to know about math: what it is, what parts are new and growing and what its importance is. Prerequisite: high school algebra and geometry; no calculus required.

**Math 1300, 1400, 1410, 1610, 1700 all fulfill the College Formal Reasoning and Analysis requirement. In addition, Math 1700 fulfills the Natural Sciences and Mathematics requirement.

Freshman Seminars Math 2020: Proving Things - Analysis (Fall) and Math 2030: Proving Things - Algebra (Spring) are one credit courses which are taken concurrently with Calculus; for more details see Math 2020-2030. These courses give an introduction to mathematical reasoning and are recommended to anyone with a serious interest in mathematics.
Remark: Before being admitted as a Math Major, you are required to have some experience with proofs (our calculus courses don't emphasize proofs). One way to satisfy this is to take either Math 2020 or Math 2030 - see the Math Major Program for more information.

Second-year courses

Math 2400, and Math 2410 are taught with a view toward applications in the Physical Sciences and Engineering.

Math 2600 is an Honors version of Math 2400 and explores the mathematical underpinnings of the subject matter in greater depth than the standard 2400 class.  

Which Courses Should I Take?

One way to evaluate your own preparation is simply by looking at old Course Final Exams. These exams are also useful for removing rust and studying for our Advanced Placement Exams.Math 1300   Math 1400   Math 1410   Math 1610   Math 2400   Math 2410  

All incoming first-year students interested in Math should take the online Canvas Math Diagnostic Placement Exam and work with their advisor to determine the appropriate place for them to begin in the sequence. Students interested in majors that require Math or who are interested in the subject should follow the advice of their advisor and recognize that Math 1300, 1400 or 1700 are typical starting courses. If you expect that your major will not require calculus and if you need only one math credit, then Math 1300 or 1700 could be the best fit.

In addition to the Canvas Math Diagnostic Placement Exam, you and your advisor might want you to brush up on their Math scores and look at a few of the Math 1300: Old Final Exams. If you get at least 75% correct on a typical Math 1300 final, then you and your advisor may decide that Math 1400 is best for you. If you get a lower score, then you and your advisor may still decide that it would be best for you to take Math 1400 -- but study a bit more to remove rust, fill-in topics you never covered, and take advantage of the Calculus Help at Penn available.

If you take Math 1400 and find that you are really swamped, then it is easy to drop back to Math 1300 (see Changing Calculus Courses below). Part of your decision also depends on how intellectually aggressive you are and how willing you are to seek help.

Students with a serious interest in mathematics and whose scores indicate it is appropriate should consider Honors Calculus classes: Math 1610 (an analogue of Math 1410) and Math 2600, an analogue of Math 2400.

Most freshmen must register before knowing how many AP credits they will get. You should register for the course you think you will take. If it turns out that you need to switch, the department will assist you.

If you need a year of calculus, but your major does not require Math 1400-1410, and in consultation with your advisor it is unlikely you will take additional calculus, you could choose Math 1400. This is a popular choice for pre-med students. Wharton students may take only Math 110 or 1410.
Note: All incoming students must take the Canvas Online Diagnostic Placement Exam and consult with their advisor about which Math course is appropriate. With the appropriate advisor approval, you may register for Math 1410 even if you have neither taken Math 1400 nor received AP credit for it and any student may take the Credit by Exam for Math 1400. [See also retroactive credit.]

If you plan to take more than a year of math, or if your major requires it, you should choose Math 1400-1410. Econ students may need Math 1410. Consult your advisor or the Math Department if you are unsure of which sequence to take.

If you get one unit of AP credit, you may start with Math 1410 and take Math 2400 in the spring. If you are serious about math you should choose a math freshman seminar. (Remember that students who come in with one unit of AP credit and take a year of calculus will be nearly halfway to a math minor by the end of the first year.) Math is used increasingly in many subjects. A good rule is to take at least one math course each semester until you have all the math you need.

Prospective Math Majors  In particular, to be admitted to the major program you are required to have taken one of the Freshman Seminars Math 2020 or Math 2030, or some related course. For more information, visit our Math Major Program web site.

Getting into the course you want: When you request a math course, you may not get the exact lecture or recitation section you want. It may take some persistence to get into the course. The Department will do their best to accommodate students, although they may not necessarily get into the section or at the time the student prefers. If you need assistance getting into a course, contact the Math Office at 215-898-8178 or email: rtoney AT and 


The Math Department begins issuing permits starting the first day of the semester. Students are advised to email (copy to request a permit. Students are advised to keep trying Penn-In-Touch prior to the start of classes. We would like to give all students adequate time to carefully consider their schedule. Someone else may drop the lecture or recitation you wish to take, thus making a place available without needing a permit.

Reminder: The Math Dept. only issues the permits; immediately after obtaining a permit you should register for both the lecture and recitation (also a lab for calculus) via Penn-in Touch, looking for the word "permit" on the registration screen. Do not go to the drop down course menu as the permit is not there.

Changing Calculus Courses  

After the add period, you may find you are taking a Calculus Course (Math 1400, 1410, 2400, 2410) that is too advanced. To give added flexibility, until the end of the drop period the Math Department also permits students in this situation to drop down from their current calculus course and add a lower sequence, for example, dropping from Math 1410 to Math 1400. This enables you to continue with the calculus sequence without losing a semester.

If you change calculus courses after the official "Add" period ends, you need to request the instructor's written permission to get into the new class. After that,  the math office will issued a permit.  Then contact your home school to get enrolled into the new class. You should also notify both your old and new T.A.'s to transfer your homework and make sure that your name is on the right class list.

NOTE: Occasionally we also permit dropping to the previous course in the same sequence until the end of the sixth week of the semester. This requires approval of the Undergrad chair and written permission of the two instructors involved.


Computer literacy is an important part of a liberal or technical education. Some Calculus classes use Maple, a powerful software package that does symbolic, graphical and numerical computations. Maple assists people with mathematical work in much the same way as word processors assist writers. You will be able to run Maple in many campus computer labs (in academic buildings, libraries and residence halls). At the bookstore Maple comes bundled with the calculus text.

No previous computer experience is required for students to take Calculus with Maple. An extensive support network is available in campus computer labs, in the residence hall Mathematics Centers and via electronic mail. For more information, please check Calculus Help.

For students who wish to run Maple on their own computers, the software will be available for purchase in the Computer Connection at a discounted price. In the Bookstore it is also "bundled" with the calculus text. Information on how to purchase Maple is usually sent by Penn's Computer Connection during the summer.

Honors Calculus

Students who are interested in Math or the Sciences or other mathematically grounded subjects (e.g., Econometrics, Engineering) might also want to consider the more challenging Honors version of Calculus II and III, Math 1610 and Math 2600 (the analogues of Math 1410 and Math 2400, respectively). These courses will cover essentially the same material as 1410 and 2400, but in more depth and involve discussion of the underlying theory as well as computations.