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Undergraduate Program

Comparing the Calculus Sequences



First YearSecond Year
MTH 171MTH 172MTH 173MTH 174
MTH 161MTH 162MTH 164 or MTH 165MTH 164 or MTH 165
MTH 141MTH 142MTH 143MTH 164 or MTH 165

Note: MTH 173-MTH 174 must be taken in order but MTH 164 and MTH 165 can be taken in either order; MTH 164 is NOT a prerequisite for MTH 165. Usually MTH 164 is taken before MTH 165 since its subject matter is more closely related to MTH 162.

There are three calculus sequences:

Each of the sequences meets the prerequisites for entering any of the engineering, science, premed, mathematics, computer science, or social science concentrations. See the placement page for more information on calculus placement.


Math 170 Sequence

Students with strong mathematical ability should consider taking the MTH 171 calculus sequence which is an honors calculus sequence for talented students interested in mathematics.

  • The MTH 171 sequence places more emphasis on the theoretical understanding of calculus in addition to teaching technical skills.
  • It carries 5 credit hours per semester rather than the standard 4 credit hours and covers all of the material on calculus, ordinary differential equations AND linear algebra contained in MTH 161 - MTH 165 and MTH 235.
  • Students completing the four semester MTH 171-174 sequence earn 20 credit hours (24 if they received AP credit) and will have completed all of the foundation requirements for a major or minor in mathematics, as well as MTH 235.
  • MTH 171 is open to students placed into MTH 161 or a higher numbered course, as well as students with AP credit. See the placement page for more information on calculus placement.
  • Students entering the 170 sequence that obtained an AP test score of 4 or higher on the calculus AB exam or a score of 3 or higher on the BC exam, are given 4 credits for the AP course, but still enroll in MTH 171.

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Math 160 Sequence

The MTH 161 - MTH 165 sequence emphasizes practice in the mathematical techniques used in science and engineering. This is the standard calculus course taught at most universities, principally to students planning to major in mathematics, computer science, physics, chemistry, or engineering. Courses are generally taken in the following order:

  • First semester - MTH 161 which covers differentiation techniques and applications
  • Second semester - MTH 162 which covers integration and applications and additional differentiation techniques
  • Third semester - MTH 164, the study of differentiation and integration techniques for functions of more than one variable
  • Fourth semester - MTH 165, linear algebra with differential equations

It is possible to switch the order of these last two courses, if knowledge of differential equations or linear algebra is needed earlier, as a prerequisite for some other science course. MTH 164 and MTH 165 can be taken in either order; MTH 164 is NOT a prerequisite for MTH 165.

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Math 140 Sequence

The MTH 141 - MTH 143 sequence covers much the same material (using the same textbook) as the MTH 161 - MTH 162 series, but at a slower pace and takes an extra semester to complete.

Many students take MTH 141 and MTH 142 during their first year and MTH 143 during the summer, either at the University of Rochester or at another university. This allows them to take MTH 164 and MTH 165 in their second year.

Students placed into MTH 140, precaluculus, move on to MTH 141 the following semester.

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