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Mathematics ---- Under Graduate Resources

Calculus, Multivariable Calculus, Linear Algebra, Intro to higher mathematics, Probability

1) The Calculus Bible, Brigham Young University (downloadable text)  

(Topics) Functions, limits, continuity, derivative with applications, integrals, techniques of integration, improper integrals, infinite series, analytic geometry, and polar coordinates.

2) Graphics for the Calculus Classroom, Douglas N. Arnold (online resource)  

(Topics) Graphics (some animated!) displaying some fundamental concepts of calculus.

3) Multivariable Calculus, George Cain & James Herod (downloadable text)  

(Topics) Euclidean 3-space, vectors and their algebra and geometry, vector-valued functions, matrices, derivatives, continuity, directional derivatives, Taylor polynomials, sequences and series, iterated integrals. Path, line, surface, and flux integrals. Theorems of Green, Gauss, and Stokes. Applications to physics.

4) Linear Algebra, Jim Hefferon (downloadable text)  

(Topics) Solving linear systems; vector spaces, linear independence, and bases; linear maps, homomorphisms and isomorphisms, change of basis, projection; determinants; Similarity, eigenvalues and eigenvectors, Jordan canonical form.

5) Basic Concepts of Mathematics, Elias Zakon (downloadable text)  

(Topics) Set theory, relations, the real number system, axioms of an ordered field, mathematical induction, Euclidean n-space and its geometry, vectors and vector spaces.

6) Introduction to Probability, Charles M. Grinstead, J. Laurie Snell (downloadable text and online resources)  

(Topics) Discrete and continuous probability distributions, combinatorics, expected value and variance, random variables, the law of large numbers, the central limit theorem, generating functions, Markov chains, and random walks.

 
 


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