If you are a MATH or an APMT major who does not have credit for Calculus I, then you should take Math 171. If your major allows you to choose either Math 151 or Math 171, then the following information may help you decide which course better meets your goals.
Math 151 is Calculus I for Engineering majors. It is a four-hour class that has a recitation that meets twice per week. On one recitation day each week, students review recently covered material and often take a quiz. On the other recitation day each week, students complete labs using Python.
Math 171 is Calculus I for Math and Science majors. It is also a four-hour class, but its recitation meets only once per week. During recitation, students review recently covered material and often take a quiz.
While Math 151 and Math 171 cover (virtually) the exact same topics, lecture examples and homework problems in Math 151 are much more applied, while Math 171 has a strong emphasis on mathematical definitions, theorems, and their proofs. Math 171 students are introduced to basic proof-writing and are expected to write definitions and proofs on exams.
In summary, Math 171 gives a more rigorous theoretical treatment of Calculus I, while Math 151 focuses on applications to physics and engineering and incorporates programming in Python.