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Core Mathematics Program

Core mathematics education at USMA includes both acquiring a body of knowledge and developing thought processes judged fundamental to a cadet's understanding of basic ideas in mathematics, science, and engineering. Equally important, this educational process in mathematics affords opportunities for cadets to progress in their development as life-long learners who are able to formulate intelligent questions and research answers independently and interactively.  More information can be found in the Core Math Book.
In the classroom, concepts are applied to representative problems from science, engineering, and the social sciences. These applications develop cadet experience in modeling and provide immediate motivation for developing a sound mathematical foundation for future studies.
The core mathematics requirement for all cadets is a three course sequence consisting of.
  1. One semester of mathematical modeling
  2. One semester of calculus
  3. One semester of probability and statistics
Cadets will be placed in the appropriate course based on previous academic preparation and aptitude for mathematics.  Cadets who have taken calculus at the college level and demonstrated mastery of the material may be able to validate the calculus requirement.  Cadets may also validate the modeling course and/or the probability and statistics course by taking a validation exam.  Cadets who demonstrate a deficiency in algebra and/or trigonometry may be required to take an additional course before entering the three-course, core math sequence.
There are six primary goals of the core mathematics program (as seen below).
  • Acquire a Body of Knowledge: Acquiring a body of knowledge is the foundation of the core math program. This body of knowledge includes the fundamental skills requisite to entry at USMA as well as the incorporation of new skills fundamental to the understanding of calculus and statistics.
  • Communicate Effectively: Students learn mathematics only when they construct their own mathematical understanding. The successful problem solver must be able to clearly articulate their problem solving process to others.
  • Apply Technology: Technology can change the way students learn. Along with increased visualization, computer power has opened up a new world of applications and solution techniques. Our students can solve meaningful real-world problems by leveraging computer power appropriately.
  • Build Competent and Confident Problem Solvers: The ultimate goal of the core math program is the development of a competent and confident problem solver. Students need to apply mathematical reasoning and recognize relationships, similarities, and differences among mathematical concepts in order to solve problems.
  • Develop Habits of Mind: Learning is an inherently inefficient process. Learning how to teach oneself is a skill that requires maturity, discipline, and perseverance. The core math program seeks to improve each cadets reasoning power by introducing multiple modes of thought. These modes of thought include deduction, induction, algorithms, approximation, implications, and others.
  • Interdisciplinary perspective:  In today’s increasingly complex world, problems leaders face require ability to consider a variety of perspectives.  Mathematical analysis and results should not be accepted without understanding the social, economic, ethical and other concerns associated with the problem. The core math program seeks to expose cadets to problems with interdisciplinary scope.  The goal is for cadets to consider what they have learned in other disciplines when faced with a problem requiring mathematical analysis.  Additionally, cadets should appropriately apply mathematical concepts to support problems faced in other disciplines.