Comparing the Calculus Sequences


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

Note: MATH 173-MATH 174 must be taken in order but MATH 164 and MATH 165 can be taken in either order; MATH 164 is NOT a prerequisite for MATH 165. Usually MATH 164 is taken before MATH 165 since its subject matter is more closely related to MATH 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 MATH 171 calculus sequence which is an honors calculus sequence for talented students interested in mathematics.

  • The MATH 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 MATH 161 - MATH 165 and MATH 235.
  • Students completing the four semester MATH 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 MATH 235.
  • MATH 171 is open to students placed into MATH 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 MATH 171.

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Math 160 Sequence

The MATH 161 - MATH 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 - MATH 161 which covers differentiation techniques and applications
  • Second semester - MATH 162 which covers integration and applications and additional differentiation techniques
  • Third semester - MATH 164, the study of differentiation and integration techniques for functions of more than one variable
  • Fourth semester - MATH 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. MATH 164 and MATH 165 can be taken in either order; MATH 164 is NOT a prerequisite for MATH 165.

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Math 140 Sequence

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

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

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

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