Any good sites for learning math?

[ToxicBug]

I starting in actuarial mathematics in September, so I would like to get ahead a bit and do some learning on my own. These are my obligatory courses:

MATH 251 Linear Algebra I (3 credits)
Matrices and linear equations; vector spaces; bases, dimension and rank; linear mappings and algebra of linear operators; matrix representation of linear operators; determinants; eigenvalues and eigenvectors; diagonalization.
MATH 252 Linear Algebra II (3 credits)
Characteristic and minimum polynomials; invariant subspaces, invariant direct sums; nilpotent operators, Jordan
canonical form; cyclic subspaces; rational canonical form; bilinear and quadratic forms; inner product; orthogonality;
adjoint operators and orthogonal operators.
MATH 264 Advanced Calculus I (3 credits)
Introductions to limits and continuity in Rn. Multivariate calculus: the derivative as a linear approximation; matrix
representation of derivatives; tangent spaces; gradients, extrema, including Lagrange multipliers, TaylorÕs formula
and the classification of critical points.
MATH 265 Advanced Calculus II (3 credits)
Implicit functions and the implicit function theorem. Multiple integrals and change of variables. Curves, surfaces
and vector calculus.
MATH 354 Numerical Analysis (3 credits)
Error analysis in numerical algorithms; solution of non-linear equations; fixed point iterations, rate of convergence.
Interpolations and approximations, Legendre polynomials. Numerical integration and quadrature.
MATH 364 Analysis I (3 credits)
Mathematical rigour: proofs and counter examples; quantifiers; number systems; Cardinality, decimal representation,
density of the rationales, least upper bound. Sequences and series; review of functions, limits and continuity.
MATH 365 Analysis II (3 credits)
Connectedness and compactness in the reals. Intermediate value theorem; extreme values for continuous functions.
Differential and integral calculus; fundamental theorem of calculus power series.
STAT 249 Probability I (3 credits)
Axiomatic approach to probability; combinatorial probability; discrete and continuous distributions; expectation;
conditional expectation; random sampling and sampling distributions.
STAT 250 Statistics (3 credits)
Point and interval estimation; hypothesis testing; Neyman Pearson Lemma and likelihood ratio tests; introduction to
correlation and regression.
ACTU 256 Mathematics of Finance (3 credits)
Measurement of interest; annuities and perpetuities; amortization and sinking funds; rates of return; bonds and
related securities; life insurance.
ACTU 257 Actuarial Mathematics I (3 credits)
Measurement of mortality; pure endowments; life insurance; net single premiums; life annuities; net annual
premiums; special topics.
ACTU 357 Actuarial Mathematics II (3 credits)
Net level premium reserves; multiple life functions; multiple decrements; the expense factor; special topics.
ACTU 457 Risk Theory (3 credits)
Applications of contingency theory in life and health insurance, annuities and pension; individual risk theory, ruin
theory.
ACTU 458 Credibility Theory (3 credits)
Credibility approach to inference for heterogeneous data; classical, regression and Bayesian models; illustrations with
insurance data.
ACTU 459 Loss Distributions (3 credits)
Probability model fitting to loss data; estimation and testing under a variety of procedures and sampling designs.
STAT 349 Probability II (3 credits)
Markov decision process and applications. Poisson process, queuing theory, inventory theory; applications.
STAT 360 Linear Models (3 credits)
Least-squares estimators and their properties. General linear model with full rank. Analysis of residuals; adequacy
of model, lack of fit test, weighted least squares; stepwise regression, Durbin-Watson statistic; one-way and two-way
analysis of variance.
STAT 460 Time Series and Forecasting (3 credits)
Time series, forecasting by trend and irregular components (using multiple regression analysis and exponential
smoothing); forecasting seasonal time series, additive and multiplicative decomposition methods, Box-Jenkins
methodology, moving average, autoregressive and mixed models.
STAT 461 Operations Research II (3 credits)
Simulation and Monte-Carlo techniques, selected topics in operations research.

So if anyone knows a good place where I could get ahead and start learning any of these topics, please go ahead and post it.

 

[ircdan]

It would be a good idea to search for the best textbooks thread I think.

Here is a link worth bookmarking.
http://www.geocities.com/alex_stef/mylist.html

This is also excellent, download the pdf titled Advanced Calculus
http://www.math.harvard.edu/~shlomo/

Chapters 1 and 2 of that book cover quite a bit of linear algebra. I think some exposure to the theory of Calculus of a single variable is very useful before reading the rest of it though.

Some good books worth buying are Calculus by Michael Spivak and Linear Algebra Done Right by Sheldon Axler. Both are excellent.

 

[ToxicBug]

Judging by the description, I've already covered all the topics in Advanced calculus I and II and I have covered some linear algebra, so I think the latter, as well as probability, analysis, and statistics are the topics that I haven't seen before.

 

[Gokul43201]

As a supplementary reference, if you need to check definitions at any point, there's always Mathworld .

 

[arildno]

What about..PF?