First Year Student Registration
Mathematics: Frequently Asked Questions
How do I satisfy the mathematics requirement if I am not yet focused on any major program?
- You may satisfy the graduation requirement by completing any course offered by the Department of Mathematics or by completing Computer Science 102 or Philosophy 200. Computer Science 102 and Philosophy 200 are not recommended for first semester students except for those intending to major in those departments. If you have earned advanced placement credit in calculus, computer science, or statistics, that credit will satisfy the Common Course of Study mathematics requirement.
- Algebra and other mathematical skills developed in high school are necessary in calculus. Therefore, if you think that you will study calculus sometime at Lafayette, the Department of Mathematics strongly advises you to register for a calculus course in your first semester, while mathematical skills are still fresh and sharp.
Should I be taking Math 125, Math 141, or Math 161? (See course descriptions here)
- Mathematics 125 is a single-semester introduction to mathematical modeling and the use of differential calculus.
- Some major programs require Mathematics 161, and some accept either Mathematics 125 or Mathematics 161 to satisfy their calculus requirements. Check your specific area of interest in the Course Selection Guide.
- If you are considering any major program that requires Mathematics 141 or 161 take the online Mathematics Placement Test A by June 19. The Mathematics Department will then use these results to help in deciding on proper course placement and will contact you by phone or through your Lafayette email account in July or August if your initial choice of mathematics course is not appropriate for your background.
- Students majoring in Economics or Policy Studies are required to take either Mathematics 141 or 161. If you do not have advanced placement credit for Mathematics 161, and are not planning on taking additional calculus courses beyond Mathematics 161, then we recommend you take Mathematics 141 (Differential Calculus and Economic Modeling). Mathematics 141 was specifically designed to help prepare students for the mathematics they will encounter as Economics or Policy Studies majors; Mathematics 141 may not be used as a prerequisite for Mathematics 162. Answering these questions or reviewing this flowchart [pdf] may provide additional guidance.
- If you are considering any major program that requires Mathematics 161 and you don’t have a strong mathematics background (as one example: if you have not had a course covering trigonometry), you may be advised to take Mathematics 125 as preparation for Mathematics 161. Similarly, you might be advised to take Mathematics 125 to help prepare you for Mathematics 141.
Advanced Placement in Mathematics; Should I be taking Math 161, 162, or 263?
- A score of 4 or 5 on the AB Calculus examination will earn credit for Mathematics 161. A score of 3, 4, or 5 on the BC Calculus examination will earn credit for both Mathematics 161 and 162. A score of 4 or 5 on the Statistics examination will earn credit for Mathematics 186. Advanced placement credit is not normally available for any other mathematics course.
- If you have earned advanced placement, the Department of Mathematics advises that you accept it. However, you are not required to accept advanced placement.
- If you have taken an A.P. examination in calculus, you will not yet know the score. Take the online Mathematics Placement Test A and Mathematics Placement Test B (and possibly Mathematics Placement Test C) by June 19. When the College receives the A.P. scores, you may be contacted with recommendations concerning changes in mathematics course selection.
- If you have had a good year-long high school calculus course, and you wish to study more calculus, you may be able to skip Mathematics 161 and take Mathematics 162 (or perhaps even Mathematics 263). Take the online Mathematics Placement Test A and Mathematics Placement Test B (and possibly Mathematics Placement Test C) by June 19. If you do well on those tests you may, with advice from the Mathematics Department, want to skip Mathematics 161 and begin your studies with Mathematics 162 (or 263), even without having received advanced placement credit. After passing Mathematics 162 (or 263), you will be able to earn credit for Mathematics 161 (or 162) by taking and passing another test at the beginning of the spring semester. Should you wish to begin your studies with Mathematics 161, though, you may do so even if you received high scores on these mathematics placement tests .
- Note that college-level calculus courses are taught at a faster pace than are high school courses. A list of topics covered in Mathematics 161 and 162 follows.
Mathematics 161 (Calculus I)
Topics
- Functions and f(x) notation.
- Limits.
- Continuity.
- Tangent lines; instantaneous velocity.
- The derivative as a limit.
- Techniques and formulas of differentiation, including trigonometric functions.
- The chain rule.
- Implicit differentiation.
- The derivative as a rate of change.
- Curve sketching techniques using the derivative: increasing, decreasing, concave up, concave down, relative maximum, relative minimum, points of inflection.
- Other curve sketching techniques: symmetry, intercepts, asymptotes.
- Maximum-minimum word problems.
- Motion along a line.
- Indefinite integrals.
- Areas as limits.
- The definite integral.
- The Fundamental Theorem of Calculus.
- Integration by u-substitution.
- Logarithmic functions: properties, graphs, calculus.
- Exponential functions: properties, graphs, calculus.
Mathematics 162 (Calculus II)
Topics
- Area between two curves.
- Finding volume by the “slicing” method.
- Inverse trigonometric functions: derivatives, integrals.
- Indeterminate forms; L’Hospital’s Rule.
- Techniques of integration: parts, partial fractions.
- Numerical integration: trapezoidal rule, Simpson’s method.
- Improper integrals.
- First order differential equations: separable, applications.
- Sequences.
- Infinite series: convergence and divergence.
- Power series: interval of convergence, Maclaurin and Taylor series.
- Parametric equations: graphs, arclength.
- Polar coordinates: graphs, area.
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