Calculus Courses

MATH 211 (Calculus)

What is MATH 211?

MATH 211 is a first-semester survey of calculus course without trigonometry. It is designed primarily for students interested in majoring in business.

An appropriate score on the IB Mathematics: Applications and Interpretations exam gives credit for MATH 211.

MATH 211 is only a prerequisite for MATH 213, and no other math courses.

• Students cannot take the MATH 211/213 course sequence and then continue into the “main” calculus sequence (MATH 222 and MATH 234). For this reason, students should take MATH 221 if there is even the slightest chance they will require or want further mathematics courses.
• Students who take MATH 211 and change their mind later will be required to go back to MATH 221. Students who complete MATH 211 but did not place directly into MATH 221 will need to go back and take the MATH 221 prerequisite coursework or retake the placement test. MATH 211 is not a prerequisite to MATH 221.

MATH 211 is primarily taken by students whose majors or programs of interest do not require MATH 221 and will accept MATH 211—such as some programs in the Wisconsin School of Business and the College of Agricultural and Life Sciences—or who are certain do not need MATH 221 to meet course prerequisites (like those for MATH 222, MATH/COMP SCI 240, PHYSICS 201 or 207, etc.).

Who should take MATH 211?

MATH 211 is great for students who…

• would like to take a calculus course but do not need MATH 221 for satisfying course prerequisites or major requirements.
• are not planning on taking the “main” calculus sequence (MATH 221, 222, or 234) or further math coursework (like MATH 340) besides MATH 213.
• have had a conversation with their academic advisor and have determined that MATH 211 is satisfactory for their needs.

Important Considerations

Pre-business students (those looking to apply to the Wisconsin School of Business but as of yet are not admitted) should strongly consider MATH 221 as an alternative to MATH 211. MATH 211 has less utility outside of the Wisconsin School of Business as it is often not accepted as an alternative course to MATH 221 for program requirements and course prerequisites. MATH 211 is also not an acceptable prerequisite course for MATH 221, and if a student takes MATH 211 they may need to complete MATH 221’s prerequisite coursework (depending on placement).

Students should have a conversation with their academic advisor if they are uncertain about which course is most appropriate for them.

MATH 213 (Calculus and Introduction to Differential Equations)

What is MATH 213?

MATH 213 is a second survey-level calculus course designed to follow MATH 211. The course covers further topics in calculus, including some topics from differential equations. As with MATH 211, this course does not use trigonometric functions.

Who should take MATH 213?

This course is required for finance majors in the Wisconsin School of Business. It is helpful preparation for economics coursework for students who have completed MATH 211 rather than MATH 221.

MATH 171/217 (Calculus with Algebra and Trigonometry I & II)

What is MATH 171/217?

MATH 171/217 is a fast-paced, two-semester sequence that combines "just in time" review of algebra and trigonometry (precalculus) with calculus topics.

Students who complete MATH 171/217 are considered to have completed the equivalent of precalculus ([MATH 112 and 113] or MATH 114) and first-semester calculus with trigonometry (MATH 221).

Who should take MATH 171/217?

MATH 171/217 is great for students who...

• are comfortable with the accelerated nature of the sequence and are confident that they can keep up with the pacing.
• are interested in a course sequence which reviews precalculus topics and also gives more immediate exposure to calculus.

If a student intends on enrolling in MATH 171/217, they should be aware that the course sequence is fast-paced and accelerated in nature. The courses are 5 credits and will require a good amount of time and focus to keep up with the pacing and be successful. If they do not wish to take a course sequence with this fast of a pace, they should consider the MATH 112/113 sequence instead.

Important Reminders

• MATH 171 is only offered in the fall, and MATH 217 is only offered in the Spring.
• Students must pass both courses in order to be awarded credit for the equivalent of MATH 114 and MATH 221, but MATH 171 does not equal MATH 114, nor does MATH 217 equal MATH 221.
  • Note that completing MATH 171 but not MATH 217 still awards course credit, but MATH 171 alone does not qualify a student for any math course outside of MATH 217.
• If a student takes MATH 171 and does not take MATH 217, and then decides to take MATH 221, they must take the prerequisite coursework for MATH 221.

MATH 221 (Calculus and Analytic Geometry 1)

What is MATH 221?

MATH 221 is a first-semester calculus course with trigonometric functions. It covers differential calculus and the beginning of integral calculus, including the calculus of exponential and logarithmic functions and applications of integration beyond area.

MATH 221 is the most commonly taken calculus course at UW-Madison, and is accepted as a prerequisite for MATH 222, which then leads to the rest of the mathematics curriculum (MATH 234, 340, etc.).

Students who earn an appropriate score on the AP Calculus AB exam (or AB subscore of the AP Calculus BC exam) earn credit for MATH 221. Selected IB and A-level exams with appropriate scores also give credit for MATH 221.

Who should take MATH 221?

MATH 221 is great for students who…

• are interested in a widely-applicable and flexible first-semester calculus course which satisfies many course prerequisites or program requirements that require calculus.
• are interested in pursuing further math coursework, such as MATH 222, MATH 234, MATH 319, MATH 340, etc.

MATH 222 (Calculus and Analytic Geometry 2)

What is MATH 222?

MATH 222 is a second-semester calculus course with trigonometric functions. It covers techniques of integration, sequences, and series (including Taylor series and power series). It also includes a brief introduction to differential equations and a brief introduction to vectors.

Students who earn an appropriate score on the AP Calculus BC exam earn credit for MATH 221.

Who should take MATH 222?

MATH 222 is great for students who…

• are interested in a widely-applicable and flexible second-semester calculus course which satisfies many course prerequisites or program requirements that require calculus.
• are interested in pursuing further math coursework, such as MATH 234, MATH 319, MATH 340, etc.

MATH 234 (Calculus–Functions of Several Variables)

What is MATH 234?

MATH 234 is a third-semester calculus course. It is the study of multivariable functions, including an introduction to vectors and concluding with topics in vector calculus (line integrals, surface integrals, and the three major theorems in this area: Green’s Theorem, Stokes’s Theorem, and Gauss’s Divergence Theorem) that are essential in physics and certain areas of engineering.

Who should take MATH 234?

MATH 234 is great for students who…

• are interested in studying calculus of more than one variable, which is frequently required by course prerequisites or program requirements that require calculus.
• are interested in pursuing more advanced mathematics courses, including possibly majoring in mathematics.

MATH 375 (Topics in Multi-Variable Calculus and Linear Algebra)

MATH 375 is an Accelerated Honors (!) course which features the role that linear algebra has in multivariable calculus. It also provides students with an introduction to proofs and proof-writing. In terms of subsequent coursework, MATH 375 generally fulfills any prerequisite that includes MATH 341.

It is assumed that students who complete this course will move on to complete the sequel course, MATH 376. (Students who complete MATH 375 and not MATH 376 are not considered to have completed the content of MATH 234! By enrolling in MATH 375 in the fall, students should be prepared to enroll in MATH 376 in the spring. Otherwise, they will need to enroll in MATH 234 in order to complete multivariate calculus.)

In summary, MATH 375:

• Is Honors-level;
• Enrollment is by permission only;
• Is accepted in both the major and certificate programs;
• Is not a course you can take if you have credit for one or more of MATH 234, 319, 320, 340, or 341;
• Is a good introduction to proofs and proof-writing;
• Covers material in MATH 320 and therefore credit for only one of MATH 320 or 375 can be applied to the math major or certificate;
• Covers material in MATH 340 and therefore credit for only one of MATH 340 or 375 can be applied to the math major or certificate;
• Covers material in MATH 341 and therefore credit for only one of MATH 341 or 375 can be applied to the math major or certificate;
• Will give students access to a number of advanced-level undergraduate math courses, although some may also require MATH 376.

More information on the MATH 375/376 sequence can be found on our Honors calculus page.

MATH 376 (Topics in Multivariable Calculus and Differential Equations)

MATH 376 is an Accelerated Honors (!) course that continues the study begun in MATH 375. This course completes the study of multivariable calculus and then focuses on differential equations. It also provides students with an introduction to proofs and proof-writing. In terms of subsequent coursework, MATH 375 generally fulfills any prerequisite that includes MATH 234 as well as courses requiring introductory background in differential equations.

In summary, MATH 376:

• Is Honors-level;
• Enrollment is restricted to those who have completed MATH 375;
• Is accepted in both the major and certificate programs;
• Is not a course you can take if you have credit for one or more of MATH 234, 319, 320, 340, or 341;
• Is good additional practice with proofs and proof-writing;
• Covers material in MATH 319 and therefore credit for only one of MATH 319 or 376 can be applied to the math major or certificate;
• Covers material in MATH 320 and therefore credit for only one of MATH 320 or 376 can be applied to the math major or certificate;
• Will give students access to a number of advanced-level undergraduate math courses.

More information on the MATH 375/376 sequence can be found on our Honors calculus page.

MATH 228 (WES-Calculus)

WES-Calculus sections are 2-credit supplementary discussion sections that students can apply for and take along with MATH 221 (typically only in fall semesters), MATH 222 (both fall and spring semesters), or MATH 234 (both fall and spring semesters).

WES-Calculus sections meet for more time than non-WES calculus discussion sections.