# Mathematics and Computer Science

Steven P. Levandosky, Ph.D.,* Associate Professor* *and Chair*

The primary goal of the programs in mathematics and computer science at Holy Cross is to enable students to become active participants in the study of fundamental and dynamic areas of human endeavor. The inherent structure and beauty of mathematics is at the core of all mathematical inquiry. Mathematics is also the language of the sciences and social sciences, and in our increasingly technology-driven society, it is part of our daily public discourse. Computing has become an indispensable tool for scientific and mathematical experimentation. The academic discipline of computer science studies algorithms, data structures, and their realization in software and hardware systems. It addresses the fundamental questions: What is computable in principle? And what tasks are algorithmically feasible? Thus the programs in mathematics and computer science are both informed by other disciplines and seek out ways that mathematics and computing have an impact on the world at large. In this context the department works toward helping students to become knowledgeable and sophisticated learners, able to think and work independently and in concert with their peers.

The department offers a number of introductory courses, a major in mathematics, a major in computer science and a minor in computer science open to students majoring in any department, including mathematics. Computing courses do not count toward the maximum number of courses that may be taken in one department for mathematics majors, nor do mathematics courses count toward the maximum number of courses that may be taken in one department for computer science majors.

## Advanced Placement

**AP Calculus:** Students who have received a score of 4 or 5 on the AP Calculus AB exam will earn one unit of credit and are advised to take Mathematics 136. Students will forfeit their AP credit if they opt to take Mathematics 133 or 135.

Students who receive a score of 4 or 5 on the AP Calculus BC exam and an AB subscore of 4 or 5 will earn two units of credit and are advised to take Mathematics 241 (Multivariable Calculus). One AP credit will be lost if the student starts in Mathematics 134 or 136, and both credits will be lost if the student starts in Mathematics 133 or 135. Students who receive a score of 3 or lower on the BC exam and an AB subscore of 4 or 5 will earn one unit of credit and are advised to take Mathematics 136. Students will forfeit their AP credit if they opt to take Mathematics 133 or 135.

**AP Statistics:** Students who have received a score of 4 or 5 on the AP Statistics exam will earn one unit of credit. Students will forfeit their AP credit if they opt to take any 100- or 200-level statistics course at the College, including Mathematics 120, Mathematics 220 (Statistics), Biology 275, Economics 249, Psychology 200, Sociology 226.

**AP Computer Science:** Students who have received a score of 4 or 5 on the AP Computer Science exam will earn one unit of credit for Computer Science 131 and are advised to take Computer Science 132. Students will forfeit their AP credit if they opt to take Computer Science 110 or 131.

**Introductory Courses:** There are a number of introductory courses that satisfy a Common Area Requirement in Mathematical Science, including Computer Science 110, Mathematics 110, and Mathematics 120. These are recommended for students who are not considering a major in mathematics, computer science, economics, accounting, the sciences and who are not aspiring to the pre-health professions.

**Calculus:** Mathematics 133, Mathematics 135, Mathematics 136 and Mathematics 241 are for students who are interested in pursuing a major in mathematics, computer science, economics, accounting, the sciences, or who are aspiring to the pre-health professions. Successful completion of Mathematics 136 fulfills any college requirement for a full year of calculus.

Students considering any of these fields may need calculus and/or statistics and should consult the specific major requirements elsewhere in the catalog. Students with little or no calculus background should enroll in Mathematics 135. Students with some calculus background should enroll in either Mathematics 135 or Mathematics 136. Students who have earned advanced placement credit should follow the guidelines above. Students who have successfully completed a year of calculus in high school, but who did not take the AP exam, or who scored a 3 or lower on the AP Calculus AB exam may consider starting with Mathematics 136, but only if they feel that they were successful in a strong high school course.

The sequences Mathematics 133, 134 and Mathematics 135, 136 are alternatives to each other. Mathematics 133 is available for students who are particularly concerned about their algebra and precalculus preparation, in addition to having had no previous calculus. Only students interested in the specific fields listed above who feel they need additional class time to adjust to college mathematics should consider Mathematics 133. Mathematics 133 and 134 meet for extra time each week and have a weekly tutorial session to provide additional support. Enrollment is by permission only.

No student may earn credit for any two of Mathematics 133 and 135, or, similarly, for Mathematics 134 and 136.

**Statistics:** Mathematics 120 is an introductory course intended for students who are not interested in pursuing mathematics, economics, biology, psychology, sociology, or the health professions. Any such students should take a 200-level statistics course instead, ideally one within their major. 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 Math 220 for health professions some time after their first year at the College.

**Computer Science:** Computer Science 110 is intended for students not majoring in mathematics, computer science, or the sciences. Computer Science 131 is for students considering further course work in computing or students majoring in any field in which computing plays a significant role.

## The Major in Mathematics

**Requirements for majors in the classes of 2017, 2018 and 2019**. Majors must take at least 10 courses in mathematics above Mathematics 133 or 135. The foundation consists of Math 134 or 136 (Calculus 2), Math 241 (Multivariable Calculus), Math 242 (Principles of Analysis), Math 243 (Algebraic Structures), and Math 244 (Linear Algebra), which are required. In addition to the required courses, majors must take five elective mathematics courses numbered above 300. At least one of these must be a project course. Majors in the class of 2017 must complete at least one course from three of the following four areas: Analysis, Algebra, Geometry/Topology, Applied Mathematics/Statistics. Majors in the classes of 2018 and 2019 must complete at least two courses from the areas of Analysis, Algebra, and Geometry/Topology, plus at least one course from the area of Applied Mathematics/Statistics. The course listings that follow show which regular upper-level mathematics courses fall within each of the areas, and majors will consult with their academic advisers no later than the end of their second year to plan their major course selections with this requirement in mind.

**Requirements for majors in the classes of 2020** and later. Majors must take at least 10 courses offered by the mathematics and computer science department. The foundation consists of Math 134 or 136 (Calculus 2), Math 241 (Multivariable Calculus), Math 243 (Algebraic Structures), and Math 244 (Linear Algebra), which are required. Majors must also take the upper-level courses Math 351 (Modern Algebra 1) and Math 361 (Real and Abstract Analysis 1). In addition to the required courses, majors must take four elective courses, at least three of which must be mathematics courses numbered above 300. Majors may take Computer Science 131, or any 200-level mathematics course numbered above 220 as one of their elective courses. At least one elective must be a project course. Math 110, Math 120, Math 133, Math 135 and Math 220 do not count toward the major.

**Project Courses**. In these courses, in place of a final exam, students work on a substantial project leading to a written report and an oral presentation. These projects provide majors with independent learning experiences, where students either investigate some topic using the tools and concepts studied in the course or explore mathematical topics beyond those covered in the course. Majors are encouraged to take advantage of the close student-faculty contact afforded by upper-division seminars, independent study, and departmental honors, which permit students to explore topics of mutual interest to students and faculty that are not part of the regular course offerings. Also, throughout the curriculum, in courses and in independent work, students are able to explore and utilize the growing relationship between mathematics and computing.

## The Major in Computer Science

Computer Science Majors must complete a minimum of 10 one-semester courses in computer science. These include seven required core courses and at least three additional upper-level (numbered 300 or above) electives. In addition, all majors must complete the equivalent of one semester of calculus; AP credit is allowed to satisfy this requirement. Prospective computer science majors are strongly encouraged to complete the equivalent of two semesters of calculus. Advanced placement credit may be used to count toward major requirements.

The required computer science core consists of three introductory, two intermediate and two upper-level courses. The introductory core courses are Computer Science 131 (Techniques of Programming), Computer Science 132 (Data Structures) and Computer Science 135 (Discrete Structures). Mathematics 243 (Algebraic Structures) may be substituted for Discrete Structures. The intermediate core courses are Computer Science 226 (Computer Systems and Organization) and Computer Science 235 (Analysis of Algorithms). The upper-level core courses are Computer Science 324 (Programming Languages Design and Implementation) and Computer Science 328 (Ethical Issues in Computer Science).

In addition to the core courses, majors are required to take at least three elective courses numbered above 300. We strongly recommend that students take at least one upper-level course carrying the project course designation. A project course allows students to combine skills and concepts they have previously learned during their undergraduate courses with new material in a complex implementation task. The project course is often scheduled for the last year of undergraduate study, where it can serve as a capstone for the undergraduate experience.

## The Minor in Computer Science

Computer Science minors must complete a minimum of 6 one-semester courses in computer science. In addition all minors must complete the equivalent of one semester of calculus.

The required computer science courses are Computer Science 131, 132, 135 (Techniques of Programming, Data Structures, Discrete Structures), Computer Science 226 (Computer Systems and Organization), plus either two additional 300-level courses or 235 (Analysis of Algorithms) and an additional 300-level course. Mathematics 243 (Algebraic Structures) may be substituted for Discrete Structures. Advanced placement credit may be used to count toward the required courses for the minor.

## Other Information

The O’Callahan Science Library in the Swords Science Center and the College’s extensive major computing facilities are described elsewhere in the Catalog. In addition, computer science and mathematics students have the opportunity to use the Department’s PC laboratory in the lower-division mathematics courses and selected computer science courses as well as the Linux network in upper-division mathematics courses and most computer science courses. The McBrien Student Lounge provides a space for students to socialize and study.

Students who are interested in teaching mathematics at the secondary school level and wish to undertake the College program leading to licensure, should consult with the Department Chair and with the Director of the Teacher Education Program. Students who are interested in majoring in mathematics and participating in the 3-2 Program in Engineering should consult with the director of that program and the Chair of the Department.

## Mathematics Honors Program

The program has two levels of distinction, Honors and High Honors. High Honors is distinguished from Honors by the successful completion of an honors thesis. Any questions concerning the program should be directed to the Department Chair.

**GPA Requirements for Honors and High Honors**: The average GPA for mathematics courses above the level of Mathematics 136 must be at least 3.50 at the end of the fall semester of the fourth year.

**Course Requirements for Honors and High Honors**: All regular course requirements for the mathematics major. In addition, for Honors, students must take at least seven courses numbered above 300. The seven courses must include at least one course with a 300-level prerequisite. Students in the classes of 2017, 2018 and 2019 must take at least one course in each of the areas of Analysis, Algebra, Geometry/Topology, and Applied Mathematics/Statistics. Note: Exceptions to some of the course requirements for Honors may be possible.

**Fourth-Year Honors Presentation**: During the fourth year all Honors majors must give an oral presentation open to the department. This may be related to their course work but it is not intended to duplicate material normally in the curriculum. It may be a presentation that originated in a project course. The goal is to ensure a certain degree of mathematical literacy among the Honors majors.

**Fourth-Year Honors Thesis for High Honors**: This is a large project typically extending over the course of the fourth year. The thesis can either consist of original research or be of an expository nature and is written under the guidance of one or more members of the department. It will culminate in an oral presentation during the spring term of the fourth year, which will be accompanied by a written report of the year’s work. Typically, a student earns one unit in each semester of the fourth year for completion of the thesis

## Computer Science Honors Program

**Course Requirements for High Honors.** Students must complete all regular course requirements for the computer science major. In addition, for High Honors, students must take six courses numbered above 300 and complete a fourth year honors thesis. This is a large project extending over the course of the fourth year. The thesis can either consist of original research or be of an expository nature and is written under the guidance of one or more members of the department.

**GPA Requirement for High Honors.** The average GPA for courses in Computer Science must be at least 3.50 at the end of the fall semester of the fourth year.