Advanced Placement in Calculus: Students who have received a score of 4 or 5 on the AP Calculus AB exam, or a subscore of 4 or 5 on the AP Calculus BC exam, will earn credit for MATH 135 and are advised to take MATH 136. Students will forfeit their credit if they opt to take MATH 133 or 135. Students who receive a score of 4 or 5 on the AP Calculus BC exam will earn credit for MATH 136 and are advised to take MATH 241 (Multivariable Calculus). Students with a 4 or 5 on the BC exam will forfeit their credit if they opt to take MATH 133, 134, 135, or 136.
AP credit in mathematics counts toward the mathematical science common area requirement. AP credit for Calculus 2 counts toward the mathematics major.
Advanced Placement in Statistics: Students who have received a score of 4 or 5 on the AP Statistics exam will earn one unit of credit for ECON 249. Students will forfeit their AP credit if they opt to take any 100- or 200-level statistics course at the College, including STAT 120, STAT 220, BIOL 275, ECON 249, PSYC 200, SOCL 226. Statistics is a part of the health professions curriculum, but many majors at the College offer their own statistics courses that are tailored to their disciplines. Health profession students are advised to wait and take the statistics course in their major, should it offer one. Otherwise, students should take STAT 220 for health professions sometime after their first year at the College.
Majors in Mathematics: Students who are considering a major in mathematics should select MATH 135 if they have not previously studied calculus. MATH 133 is available for students who are particularly concerned about their algebra and pre-calculus preparation who have not previously studied calculus. Students who have successfully earned credit for MATH 135 or who successfully completed a calculus course in high school should choose MATH 136. Students who have earned credit for MATH 136 or who have successfully completed a year of AP calculus in high school should choose MATH 241. MATH 133 and MATH 135 do not count toward the major, so students who are ready for Calculus 2 are encouraged to start there.
Advisory Notes: (1) We do not recommend calculus for students unless it is required for their major or for health professions. Students who are not planning to major in an area that requires calculus should consider CSCI 110 (only available in the third and fourth year), MATH 110 (topics courses vary each semester and are primarily intended for second, third, and fourth years) or STAT 120 (available only after a major has been declared, and only in the second, third, and fourth years). These courses fulfill the Mathematical Science common area requirement and are not geared toward science, economics, or math majors.
(2) Students with little or no calculus background should enroll in MATH 135. Students who have successfully completed one year of calculus should consider enrolling in MATH 136. Students will be allowed to drop back to MATH 135 during the first few weeks of the semester (even after the add/drop deadline), if it turns out that MATH 136 is not the best fit. Students who have earned Advanced Placement credit should follow the guidelines above. MATH 133 is available for students who are particularly concerned about their algebra and pre-calculus preparation, in addition to having had no previous coursework in calculus. Students interested in MATH 133 should consult with their class dean or the chair of mathematics and computer science (Professor Eric Ruggieri, eruggier@holycross.edu), as admission is by permission only. MATH 133, MATH 135, MATH 136, and MATH 241 are for students who are interested in pursuing a major in economics, mathematics, the sciences, or who are aspiring to the health professions. Only students interested in these areas who feel they need additional class time to adjust to college mathematics should consider MATH 133.
Courses
MATH 133
Calculus 1 with Fundamentals
Common Area: Mathematical Science
A version of Mathematics 135 that is designed for students who require more class time to make the transition to college-level Mathematics. See the description of Introductory Courses before choosing this course. See the description of Mathematics 135 for the course content. This course meets five hours per week.
MATH 135
Calculus 1
Common Area: Mathematical Science
This is the standard version of Calculus at the College. Considers the calculus of real-valued functions of one variable for students who are planning further course work in Mathematics, a major in the social or physical sciences, or the premedical program. Emphasis is placed on a conceptual understanding of calculus, presenting material from symbolic, numerical, and graphical points of view. The concepts of limit, continuity, and derivative are developed and applied to algebraic, logarithmic, exponential and trigonometric functions.
Applications of the derivative are explored. This course meets three hours per week.
MATH 136
Calculus 2
Common Area: Mathematical Science
Considers the calculus of real-valued functions of one variable for students who are planning further course work in Mathematics, a major in the social or physical sciences, or the premedical program. Emphasis is placed on a conceptual understanding of the calculus, presenting material from symbolic, numerical, and graphical points of view. Course content includes the theory, evaluation, and applications of integration, sequences and series including Taylor polynomials and series, and an introduction to ordinary differential equations. This course is the prerequisite for Mathematics 241. This course meets four hours per week.
MATH 199-S01
Discrete Mathematics
Common Area: Mathematical Science
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions). Objects studied in discrete mathematics include integers, graphs, and statements in logic. By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry. Discrete objects can often be enumerated by integers; more formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets (finite sets or sets with the same cardinality as the natural numbers).
MATH 241
Multivariable Calculus
Common Area: Mathematical Science
A study of the calculus of functions of several variables. Concerns the theory and applications of differentiation and integration of functions of several variables, vector fields, line integrals, Green's theorem. This course meets four hours per week.
MATH 243
Mathematical Structures
Common Area: Mathematical Science
An introduction to the primary algebraic and analytic structures in abstract mathematics. Emphasis is placed on using the language of sets, equivalence relations and functions, and on developing techniques of proof, including elementary logic and mathematical induction, basic group theory, and limits.