## Advanced Core Mathematics Program

## Advanced Core Mathematics Program

## Mathematical Sciences (left)

## 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 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. To complete the core mathematics requirement for graduation, students will then take Probability and Statistics (MA206) or Advanced Probability and Statistics (MA256) 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, second order differential equations, systems of first order linear and non-linear differential equations, and Laplace Transforms. This course also introduces topics such as matrix algebra and numerical methods. The primary software system is Wolfram Mathematica which will be used to enhance understanding of course material.

MA 255 - Advanced Multivariable Calculus

This course consists of an advanced coverage of topics in multivariable calculus with a focus on interdisciplinary applications. Topics include a detailed study of vectors and geometry of space, vector functions, partial derivatives, multivariable integration, and vector calculus. Additional topics include an introduction to sequences and series. 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 qualify for placement 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. The core mathematics graduation requirement consists of a mathematical modeling course (MA103 or MA153), a college-level Calculus course (MA104, MA205, or MA255), and a probability and statistics course (MA206/MA256). There are two primary core mathematics tracks at West Point: the Advanced Core Mathematics Program and the Core Mathematics Program. Students enrolled in the Advanced Core Math Program take MA153, MA255, and MA206/MA256 to meet their core math requirement. Students in the Core Math Program take MA103, MA104 (or MA205), and MA206/MA256 to satisfy their core math requirement. Any of these courses may be validated based pon previous college transcripts, validation exams, or additional interviews. Students who qualify for placement into the Advanced Core Mathematics Program but who choose not to enroll in the Advanced Core Mathematics Program will be placed into the Core Mathematics Program. However, they will be given an opportunity to validate MA104 (Calculus I) by passing a validation exam administered during the second week of the Fall semester. Students who are successful will then be placed into MA205 (Calculus II) for the Spring semester.

Q. What suggestions do you have for how I can best prepare for the placement exam?

A. Review material from your previous calculus course, but note that we make placement decisions based on your knowledge of AP Calculus AB. There are a plethora of resources at __APCentral/AP Calculus AB__. Khan Academy also has some great free resources __here__.

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 benefit is that you will be exposed to topics not covered in the Core Math Program such as modeling using 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. Additionally, 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.

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

A. Acceptance into the program is based on Summer Calculus Placement Exam scores, SAT/ACT Math scores, Advanced Placement (AP) Calculus scores (if applicable), and any college level calculus grades.

Q. What is the Summer Calculus Placement exam?

A. The Summer Calculus Placement Exam is two hours long and tests your comprehension of single-variable calculus concepts (typically topics covered in Calculus I and Calculus II courses) without the use of technology (i.e., graphing calculator). This voluntary exam is part of the New Cadet Testing that is administered remotely from mid-May to mid-June before the start of Cadet Basic Training. If you choose to take the exam, we assume that signifies your intent to enroll in the Advanced Core Mathematics Program should you achieve a passing score. 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 3 on the BC exam or a 4 on the AB exam would be a good candidate for our program. Candidates who score even higher would be considered more competitive for entry!

Q. I wasn't planning on taking either AP Calculus exam - can I still take the Calculus Placement 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 Calculus Placement 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 Calculus Placement Exam.

Q. My school offers the IB program and AP class opportunities are limited. Do you consider IB scores in your selection process?

A. While IB scores are not considered for selection, there have been several students from an IB background who achieved success in our program. We highly recommend that you take college level calculus courses if offered at your location.

Q. How can I get more information?

A. You can email MAJ Tom Mussmann or MAJ Devon Zillmer with any additional questions.