Undergraduate Program Pre-concentration: The First Two Years The ideal high-school background for a student who intends to concentrate in mathematics (or science or engineering) includes one and one-half years of algebra, one year of geometry, one-half year of trigonometry, and one year of pre-calculus and/or calculus. Inclusion of a high-school calculus course is not essential; courses 115 and 185 do not assume previous calculus experience. A student whose background is less thorough may need to begin college mathematics with Math 105 (Data, Functions and Graphs) and should expect to spend at least one extra semester to complete a mathematics concentration. Prospective mathematics concentrators may choose from a variety of entry-level courses: Math 115 (Calculus I) Math 156 (Applied Honors Calculus II) Math 174 (Proofs in Geometry) Math 175 (Introduction to Cryptology) Math 185 (Honors Anal. Geom. and Calc. I) Math 295 (Honors Mathematics I) Math 115 is the standard course taken by the majority of students intending to concentrate in mathematics, science, or engineering. Together with Math 116 and 215, it provides a complete introduction to the concepts and methods of calculus. This sequence stresses problem-solving and applications rather than theory and proof, and features cooperative learning and graphing calculators. Following Math 215 all students intending to concentrate in mathematics should elect Math 217 (Linear Algebra) rather than Math 216 (Introduction to Differential Equations). Math 216 is not intended for mathematics concentrators, who generally take Math 316 (Differential Equations) after completing Math 217. Math 174 (Proofs in Geometry) and Math 175 (Intro. to Cryptology) require permission from the honors mathematics placement advisor, but are also open to students not enrolled in the LS&A Honors Program. The sequence Math 185-186-285-286 is an introduction to calculus at the honors level. Math 185 (Honors Calculus I) presupposes a higher level of accomplishment in high school math courses and covers somewhat more of the theory behind the calculus. Math 186 is usually followed by Math 285; after completion of Math 285, a prospective honors concentrator should take Math 286 followed by Math 451; other concentrators should follow the sequence 217-316. Admission to Math 185 requires permission of the honors placement advisor. Math 295 (Honors Mathematics I) together with the succeeding courses Math 296-395-396 provide an intensive introduction to theoretical mathematics. From the beginning, students are exposed to abstract concepts. These courses require a higher level of interest and commitment than either of the other introductory sequences. The student who completes Math 396 is prepared to explore the world of mathematics at the advanced undergraduate and graduate level. Admission to Math 295 requires permission from the honors mathematics placement advisor, but is also open to students not enrolled in the LS&A Honors Program. Students who enter the University with a score of 4 or 5 on either the AB or BC Advanced Placement exam in Mathematics have several additional options. You may elect any of the courses described above or Math 116, the standard second-semester calculus course. Math 156 is a second-semester calculus course designed for students interested in science or engineering with AP scores of 4 or 5 on the AB exam and uses MAPLE. A student with a score of 4 or 5 on the BC exam may also choose to enroll in Math 215 or Math 285. Advanced Placement credit is granted in varying amounts as explained by a memo available online.