**Advanced Core Mathematics Program**

**What is the Advanced Core Mathematics Program?**The Advanced Core Mathematics Program is a voluntary two-semester advanced mathematics sequence for selected cadets who have validated single variable calculus and demonstrated strength in the mathematical sciences. It is designed to provide a foundation for the continued study of mathematics, technology, sciences, and engineering. Students in the program study Mathematical Modeling and Introduction to Differential Equations (MA153) during their first semester and Advanced Multivariable Calculus (MA255) in their second semester. Students will then take Probability and Statistics (MA206) in the fall of yearling year.

**Course Descriptions**

*MA153 - Mathematical Modeling and Introduction to Differential Equations*

This course emphasizes the interaction between mathematics and the physical sciences through modeling with differential equations. Topics include a study of first order differential equations, first order difference equations, Laplace transforms, second order differential equations, series solution techniques, systems of first order linear equations, numerical methods, and nonlinear equations and stability. An understanding of course material is enhanced through the use of Mathematica (computer algebra system) and Excel (spreadsheet).

*MA 255 - Advanced Multivariable Calculus*

This course consists of an advanced coverage of topics in multivariable calculus. Topics include a detailed study of vectors and geometry of space, vector functions, partial derivatives, multiple integrals and vector calculus. An understanding of course material is enhanced through the use of Mathematica (computer algebra system).

**Frequently Asked Questions**

*Q. How do I know if I should try to validate single variable calculus and enroll in the Advanced Core Mathematics Program?*

A. You should seriously consider this program if you have already taken, or are currently taking, Calculus I, II, or III at the high school or college level.

*Q. Can I validate single variable calculus but not enroll into the Advanced Core Mathematics Program?*

A. No. There are two primary core mathematics tracts at West Point: the Advanced Core Mathematics Program and the Core Mathematics Program. Students enrolled in the Advanced Core Math Program take three math courses as part of their core math requirement (MA153, MA255, & MA206). Students in the Core Math Program also must take three math courses to satisfy their core math requirement (MA103, MA104, & MA206). There is also a four-course track for students who start the core program with pre-calculus: (MA100, MA103, MA104, & MA206).

*Q. I have heard the core math program at West Point is difficult enough without taking advanced courses. What are the benefits of the Advanced Core Mathematics Program?*

A. The immediate benefit of enrolling in the Advanced Core Math Program is the opportunity to optimize your academic and intellectual development at West Point. The second, and most important, benefit is that you will be exposed to topics not covered in the Core Math Program such as advanced vector calculus and a full semester devoted to differential equations. This is particularly important if you are considering a math, science, or engineering major as you will be better prepared for the advanced classes you will take in your second, third and fourth years. Enrollment in the Advanced Core Math Program enables you to validate MA205, which would be a required course for most math, science, engineering, and economics majors. As a result, you would be able to begin taking courses in your major a semester early or possibly take an additional elective of interest to you. Additionally, those who excel in the Advanced Core Math Program have the opportunity to validate MA364, a required course for most engineering majors, thus freeing up a second additional elective opportunity.

*Q. How are students selected for the Advanced Core Mathematics Program?*

A. Acceptance into the program is based on your Summer Validation Exam score, your SAT/ACT Math scores, any AP Calculus scores, and any college level calculus grades.

*Q. What is the Summer Validation exam?*

A. The Summer Validation Exam is two hours long and tests your comprehension of single-variable calculus concepts (typically topics covered in college Calculus I & II courses) without the use of technology (i.e. graphing calculator). The exam is offered during the first week of Cadet Basic Training (CBT) and signifies your intent to enroll in the Advanced Core Mathematics Program. Therefore, you must take this exam in order to be considered for the program.

*Q. Does taking the AP Calculus BC exam offer any advantages over the AP Calculus AB exam with regards to validation?*

A. The Calculus BC exam covers several topics not tested in the Calculus AB exam. These topics include integrals in polar coordinates, sequences and series, as well as some additional integration techniques (such as integration by parts and integration by partial fractions). Studying for and taking the Calculus BC exam would give you a definite advantage in the advanced mathematics program.

*Q. If I take the AP Calculus BC exam will my AB sub-score be equal to an AB exam score?*

A. Yes, your AB sub-score is treated exactly the same as a Calculus AB exam score.

*Q. What is considered a "good" AP Calculus exam score?*

A. A candidate who scores a 4 or 5 on the AB Exam or a 3, 4, or 5 on the BC exam would be a good candidate for the advanced mathematics program.

*Q. I wasn't planning on taking either AP Calculus exam - can I still take the validation exam and be accepted into the Advanced Core Mathematics Program?*

A. Yes. Although we strongly encourage our students to take an AP Calculus exam we understand that this is not possible in every case. Students with no AP Exam scores on file can be accepted into the program based on their Summer Validation Exam score, their SAT/ACT Math scores, and any college level calculus grades. Historically, students accepted into our program without an AP Calculus exam score performed very well on the Summer Validation Exam.

*Q. How can I get more information?*

A. You can email **MAJ George Hughbanks** or **CPT Jon Paynter** with any additional questions.