Mathematics Resources

As detailed in the CSUN Conferences between 2010 – 2016, we will be sharing & accommodating Mathematics in Higher Education resources here.

The following list is commonly used within the accessing maths and science field and is to be shared amongst students and teachers alike.

Faculty of Mathematics Cambridge University – https://www.maths.cam.ac.uk/

London Mathematical Society – https://www.lms.ac.uk/

  • MathType exports as XHTML+MathML
  • Chemistry, physics, or engineering
  • Audio graphing calculator Windows software application
  • Nasa – MathTrax

Mathematics Books

  1. Mathematical Methods for Physics and Engineering by K.F. Riley, M.P. Hobson, and S.J. Bence
    • A comprehensive resource for applied mathematics in physics and engineering contexts.
  2. Principles of Mathematical Analysis by Walter Rudin
    • A classic text for rigorous real analysis, often referred to as “Baby Rudin.”
  3. Introduction to the Theory of Numbers by G.H. Hardy and E.M. Wright
    • Foundational work for understanding number theory concepts.
  4. Linear Algebra Done Right by Sheldon Axler
    • A conceptual approach to linear algebra with minimal reliance on determinants.
  5. Algebra by Serge Lang
    • A detailed and rigorous resource for modern algebra.
  6. Concrete Mathematics by Ronald Graham, Donald Knuth, and Oren Patashnik
    • Blends discrete mathematics with combinatorics and computer science applications.

Online Mathematics Platforms

  1. arXiv.org
    • Repository for preprints in mathematics, including algebra, analysis, topology, and applied fields.
  2. MathWorld
    • Comprehensive online encyclopedia of mathematics by Wolfram Research.
  3. Paul’s Online Math Notes
    • Clear and concise notes on calculus, differential equations, and algebra.
  4. MIT OpenCourseWare
    • Free access to mathematics courses such as Linear Algebra, Real Analysis, and Computational Mathematics.
  5. Stack Exchange Mathematics
    • A community-driven platform for asking and answering mathematics-related questions.

Maths Journals

  1. Journal of the American Mathematical Society (JAMS)
    • Publishes research papers of the highest quality across all areas of mathematics.
  2. Annals of Mathematics
    • Renowned for presenting groundbreaking work in theoretical and applied mathematics.
  3. SIAM Journal on Applied Mathematics
    • Focuses on the application of mathematics to problems in science, engineering, and society.
  4. Mathematical Reviews (MathSciNet)
    • Provides detailed reviews and summaries of mathematical research papers.
  5. The Electronic Journal of Combinatorics
    • Dedicated to research in combinatorial mathematics.

Mathematics Software and Tools

  1. MATLAB
    • Widely used for numerical computation, simulation, and visualization.
  2. Wolfram Mathematica
    • Comprehensive tool for symbolic computation, algebra, and visualization.
  3. LaTeX
    • Essential for writing academic papers with advanced mathematical notation.
  4. GeoGebra
    • Interactive geometry, algebra, and calculus application.
  5. SageMath
    • Open-source mathematics software that integrates many existing tools.

Mathematics Summary for Academics

Key Areas of Mathematics

  1. Pure Mathematics
    • Abstract Algebra: Study of algebraic structures like groups, rings, and fields.
    • Real and Complex Analysis: Foundations of calculus, integration, and series in real and complex domains.
    • Topology: Study of properties preserved under continuous transformations.
    • Number Theory: Exploration of integers, prime numbers, and modular arithmetic.
  2. Applied Mathematics
    • Numerical Analysis: Techniques for approximating solutions to mathematical problems.
    • Optimization: Study of maximizing or minimizing functions under constraints.
    • Mathematical Physics: Application of mathematics to solve problems in physics.
    • Dynamical Systems: Study of systems that evolve over time.
  3. Interdisciplinary Fields
    • Computational Mathematics: Intersection of mathematics and computer science.
    • Data Science and Statistics: Analysis of data using mathematical tools and probabilistic models.
    • Mathematical Biology: Application of mathematics to model biological systems.

Emerging Trends in Mathematics

  1. Machine Learning and AI
    • Mathematics underpins the algorithms and optimization techniques used in artificial intelligence.
  2. Quantum Computing
    • Quantum mechanics and linear algebra play a significant role in developing quantum algorithms.
  3. Mathematical Modeling of Epidemics
    • Applied mathematics has been crucial in modelling the spread of diseases like COVID-19.
  4. Cryptography
    • Advances in number theory and algebra are driving the development of encryption systems.

These resources and summaries should serve as a robust foundation for academics engaged in mathematics research, teaching, or interdisciplinary applications. Let me know if you need more focused recommendations!