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 116 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 year, Second 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 firstyear 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. Passing the external Advanced Placement BC Exam administered by the College Entrance Examination Board with a score of 5 gives credit for Math 104. Lower scores on the BC Exam receive no course credit. No credit is given for the AB Exam. First year students who wish to take Math at Penn and have credit for Math 104 should still take the Canvas Math Diagnostic Placement Exam.
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 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. Thus, you have lost nothing.
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 and students can also take credit by exams for Math 104, Math 114, Math 115, Math 240 and Math 241.
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 students may 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.
You can take more than one exam. For example, if you pass the first exam in Math 104, you could take Math 114 in the next exam (usually given the next day). 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: Due to COVID19 for Spring and Fall 2020 only students can receive retroactive credit based on "Pass" (if taken P/F) or grade of B. For classes taken in Fall 2017 or later, if you get a grade of "B" or better in math 114, 115, 116 or Math 240 at Penn, you may receive retroactive credit for Math 104 only. If you pass Math 260 with a "B" or higher, you may get retroactive credit for either 116 or 104. Beginning with the Class of 2021, if you pass Math 241 at Penn with a grade of "B" or higher, you may receive retroactive credit for either Math 104, 114 or 240. For students who enrolled at Penn in the Class of 2020 or earlier, we will still allow you to get retroactive credit for Math 114 if you received a grade of "B" or better in Math 240. Note: You cannot receive retroactive credit by passing our Fall or Spring AP exams or by receiving transfer credit for a calculus course, the course must be taken at Penn. DUE TO COVID19, send an email to rtoney@math.upenn.edu and include your PID# to request retroactive credit).
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 103) 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 highschool 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 101type 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. Due to COVID, send an email to rtoney@math.upenn.edu with your PID#)
Description of Courses
Firstyear 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.
There are a number of available alternatives among the firstyear courses.
A halfcredit course Math 101, Algebra and Trigonometry, can be used for students who need additional algebra and trigonometry and as a preparation to Math 103. Math 101 is only offered online through the College of Liberal and Professional Studies, and interested students should consult with their academic advisor.
Math 103, 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 104, 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 secondsemester Calculus courses. Students are advised to check their major department or their program for the specific requirement. In general, Math 114, Multivariable Calculus is taken by students in the natural sciences, engineering and economics. Math 114 prepares students for the more advanced Calculus courses Math 240 and 241. Those who do not plan to take Math 240 may still want to consider taking Math 114. Wharton students can take Math 114 or Math 115.
Math 116 is an Honors version of Math 114 and explores the mathematical underpinnings of the subject matter in greater depth than the standard 114 class.
Math 115, Multivariable Calculus with Probability and Matrices is for students who do not plan to take more calculus such as Math 240, and want an introduction to probability and matrices.
You cannot receive credit for both 114 and 115. The credit for Math 114 satisfies requirements specifying Math 115. You may not take Math 103 if you already have credit for Math 104.
Math 170 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 180 Analytical Methods in Economics, Law, and Medicine. This course gives elementary applications of decision analysis, game theory, probability and statistics to issues in areas such as accounting, contracting, finance, law, and medicine. This course is suitable for both prelaw and premed students. Prerequisite: high school algebra and geometry; no calculus required.
Math 103, 104, 114, 115, 116, 170 and Math 180 all fulfill the College Formal Reasoning and Analysis requirement. In addition, Math 170 fulfills the Natural Sciences and Mathematics requirement.
Freshman Seminars Math 202: Proving Things  Analysis (Fall) and Math 203: Proving Things  Algebra (Spring) are one credit courses which are taken concurrently with Calculus; for more details see Math 202203. These courses give an introduction to mathematical reasoning and are recommended to anyone with a serious interest in mathematics. [These courses replace the old Math 200201 and Math 204205 Freshmen Seminars.]
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 202 or Math 203  see the Math Major Program for more information.
Secondyear courses
Math 240, and Math 241 are taught with a view toward applications in the Physical Sciences and Engineering.
Math 260 is an Honors version of Math 240 and explores the mathematical underpinnings of the subject matter in greater depth than the standard 240 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 103 Math 104 Math 114 Math 115 Math 116 Math 240 Math 241 
All incoming firstyear 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 103, 104, 170, or 180 are typical starting courses. If you expect that your major will not require calculus and if you need only one math credit, then Math 103, 170, or 180 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 103: Old Final Exams (no calculators, but you can use one 8.5×11 sheet with notes  so there is no pressure to memorize formulas). If you get at least 75% correct on a typical Math 103 final, then you and your advisor may decide that Math 104 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 104  but study a bit more to remove rust, fillin topics you never covered, and take advantage of the Calculus Help at Penn available.
If you take Math 104 and find that you are really swamped, then it is easy to drop back to Math 103 (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 116 (an analogue of Math 114) and Math 260, an analogue of Math 240.

If you need a year of calculus, but your major does not require Math 104114, and in consultation with your advisor it is unlikely you will take additional calculus, you could choose Math 104115. This is a popular choice for premed students. Wharton students may take only Math 114 (not Math 115).
Note: All incoming students must take the Canvas Online Diagnostic Placement Exam and consult their advisor about which Math course is appropriate. With the appropriate advisor approval, you may register for Math 114 (or 115) even if you have neither taken Math 104 nor received AP credit for it and any student may take the Credit by Exam for Math 104. [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 104114. Econ students may need Math 114. 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 114 and take Math 240 in the spring  or just take Math 115 in the fall. 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 202 or Math 203, 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 2158988178 or email: rtoney AT math.upenn.edu).
Permits
The Math Department begins issuing permits starting the first day of the semester. Due to COVID19, students are advised to email rtoney@math.upenn.edu (copy airey@math.upenn.edu) to request a permit. Students are advised to keep trying PennInTouch 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 Dept. only issues the permits; immediately after obtaining a permit you should register for both the lecture and recitation via Pennin Touch, looking for the word "permit" in the upper righthand corner of the registration screen.
Changing Calculus Courses
After the add period you may find you are taking a Calculus Course (Math. 104, 114, 115, 240, 241) 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 their current Calculus Course and add the previous course in the sequence, for example, dropping from Math 114 to Math 104. 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 own school to be 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 written permission of the two instructors involved.
Computers
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 116 and Math 260 (the analogues of Math 114 and Math 240, respectively). These courses will cover essentially the same material as 114 and 240, but in more depth and involve discussion of the underlying theory as well as computations.