The Applied Mathematics Department provides a collection of self-guided, asynchronous learning modules designed to support student success in graduate-level mathematics at the Naval Postgraduate School. Use these resources in your first couple of weeks at NPS as they strengthen foundational knowledge, reinforce key concepts, and address common challenges observed among NPS learners. The format is intentionally flexible and on demand, allowing students to review material when needed and progress at their own pace. 

Why Study Mathematics?

Mathematics is not only a technical subject, but a foundational way of thinking that supports logical reasoning, precision, abstraction, and problem-solving across engineering, computing, economics, and the sciences.


Mathematics is not just a subject—it is a way of thinking.

Module Collections

Whether you are returning to formal academics or sharping your skills for advanced studies, these self-paced modules can help bridge the gap between where you are and where you need to be. Our modules are designed to:

  • Support review of foundational topics essential for graduate mathematics coursework at NPS. 
  • Target common mistakes and conceptual gaps frequently encountered by adult learners returning to mathematics. 
  • Provide concise explanations and self-paced opportunities for practice and reflection. 
  • Promote analytical habits that strengthen confidence and independent problem-solving. 

Study Strategies

These resources help students approach graduate mathematics with effective habits, realistic planning, and stronger test-taking and review strategies.  Along Effective Study and Test-Taking Strategies, the self guided content complements NPS Refresher Courses learning on these topics.


Review Videos

This set of short videos reinforces foundational algebra concepts with emphasis on conceptual clarity and correction of frequent errors. Topics include:

  • Story of Numbers
  • Undefined Operations in Real Numbers
  • Common Algebraic Mistakes
  • Logarithms as Exponents

Discrete Mathematics Videos

These modules develop formal reasoning, proof habits, and mathematical communication through focused instruction on logic and proof techniques. Modules include:

Logical Reasoning

  • Conditional Statements Parts 1 - 4

Proof Techniques

  • Proofs of Mathematical Statements Part 1
  • Methods of Proof Parts 2 & 3
  • Proof by Contraposition
  • Proof by Contradiction

Mathematical Induction

  • Mathematical Induction Parts 1 & 2

Student Experience

Participants engage in a self-guided learning experience designed to support independent progress.

  • Self-paced exploration of structured modules.
  • Identification and correction of common mistakes observed among NPS adult learners.
  • Targeted video content that addresses conceptual gaps.
  • Guided resources that support independent problem-solving.
  • Development of confidence through continuous practice and reflection.

Through these resources, the Applied Mathematics Department supports not only mathematical proficiency,
but also the development of analytical thinking essential for success across disciplines.