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Library of Math

  1. Mar 26, 2005 #1
    didn't know where it would be best to post this. but here ya go...

    http://www.libraryofmath.com/

    seems like it might be a good resource for anyone who needs help with math. I haven't used it much myself, but anyone who has or does can say whether or not its useful.
     
  2. jcsd
  3. Mar 26, 2005 #2

    matt grime

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    i needed to omit the www in the link to get the page. here is its (full, apparently) list of topics should anyone want look any of them up. i trust me cutting and pasting it here is acceptable. appears to be of use to freshman and sophmore years in the US (mathwonk, if you're reading, we probably shouldn't read them in case it provokes too many "No! That's not how to think about it" feelings)

    Calculus I
    # The Limit of a Function
    # Continuity of a Function
    # Introduction to the Derivative
    # Techniques of Differentation
    # Applications of the Derivative
    # l Hopitals Rule
    # Curve Sketching
    # Introduction to the Integral


    Calculus III
    # Vectors in Space
    # Curves and Surfaces in 3D
    # Vector-Valued Functions
    # Limits and Continuity of Vector Functions
    # Derivatives and Integrals of Vector Functions
    # Tangent and Normal Vectors of Vectors Functions
    # Functions of Several Variables
    # Limits and Continuity of Functions of Several Variables
    # Partial Derivatives of Functions of Several Variables
    # Differentiability of Functions of Several Variables
    # Chain Rules
    # Derivatives of Functions of Several Variables
    # Extrema of Functions of Several Variables
    # Double Integrals
    # Triple Integrals
    # Vector Fields
    # Line Integrals
    # Fundamental Theorem for Line Integrals
    # Greens Theorem
    # Surface Integrals
    # Stokes Theorem
    # Divergence Theorem


    Euclidean Geometry
    # Euclid Common Notions Postulates And Definitions
    # Euclid Book One
    # Hilbert Undefined Terms And Definitions
    # Hilbert Incidence Axioms
    # Hilbert Betweenness Axioms
    # Hilbert Congruence Axioms
    # Interior And Exterior Angles With Hilbert Axioms
     
  4. Mar 26, 2005 #3
    hmm, ok, i'm not sure where you got that.... but here's what i see as a list of topics... i edited the really long descriptions. But you can all get an idea of whats going on...

    REAL NUMBERS
    The field axioms and properties of real numbers including the subsets: whole numbers, integers, rational numbers, and irrational numbers. The decimal representation of real numbers with special constants to many digits and in different bases...
    TABLES OF FUNCTIONAL VALUES
    Tables of values of real valued functions of a real variable; for example, trigonometric, logarithmic, and exponential tables are included, as well as, many more transcendental functions. Many complex valued functions are also tablulated...
    GRAPHS OF FUNCTIONS
    Graphs of real valued functions of a real variable; for example, lines, quadratic, cubic, polynomial, rational, trigonometric, logarithmic, and exponential are included, as well as, many more transcendental functions. Many complex valued functions are also graphed. Many animation are included...
    COMPLEX NUMBERS
    The field axioms, operations on complex numbers, and properties of complex numbers including the subsets: imaginary numbers and the Gaussian intgers. The exponential (and trigonometric) representation of complex numbers with special constants to many digits...
    COLLEGE ALGEBRA
    Linear, quadratic and higher order polynomial equations and inequalities solved algebraically, graphically and numerically; graphs and operations on relations and functions; real and complex zeros of polynomials and rational functions; exponential and logarithmic functions; systems of linear equations; matrices...
    TRIGONOMETRY
    Trigonometric functions, radian measure, solution of triangles, graphs of trigonometric functions, trigonometric identities and equations, and complex numbers...
    ANALYTIC GEOMETRY
    Vectors, lines in two dimensions, circles, conics, transformation of coordinates, polar coordinates, parametric equations, and the solid analytic geometry of vectors, lines, planes, cylinders, spherical and cylindrical coordinates....
    CALCULUS I
    Calculus I consists of the concepts of limit, continuity, differentiation and integration; and the applications of these concepts. In general.... [i edited, its long, it just says a lot about what calc 1 is.]
    CALCULUS II
    Calculus II is intended to complete the basic introduction to calculus for students in the mathematical and physical sciences, and for others who require a solid introduction to calculus; and consists of the applications of integration, techniques of integration, parametric equations, polar coordinates, sequences and series.... [edit this one too... it says a lot]
    CALCULUS III
    Calculus III consists of the concepts of partial differentiation, multiple integrals (with applications), line integrals, Green’s Theorem, surface integrals, Stokes’ Theorem, and the divergence theorem.... [lots again]
    DIFFERENTIAL EQUATIONS
    Ordinary differential equations with emphasis on the solutions and analysis of first and higher order differential equations drawn from fields of physics, chemistry, geometry, and engineering...
    LINEAR ALGEBRA
    Solving systems of linear equations, matrix operations, determinants, vector spaces, linear transformation, orthogonality, Gram-Schmidt process, projections, and eigenvalues and eigenvectors...
    PROBABILITY
    Permutations, combinations, events and their probabilities, Bayes formula, random variables, probability distributions, expected value, functions of random variables, moment generating functions, central limit theorem and its role in statistics...
    STATISTICS
    Descriptive statistics, relationships between variables, interpretation of data and graphs, rudiments of probability, elementary statistical models, hypothesis testing, inference, and estimation. Topics in multivariate data analysis with applications in various areas of interest, including multiple regression, analysis of experimental designs, covariate adjustment, non-linear regression and the use of standard multivariate statistical packages. A comprehensive study of basic statistical methods. Topics include descriptive statistics, numeracy, report writing, basic probability, experimental design and analysis....
    FINANCIAL MATHEMATICS
    Presents material covered in a traditional algebra course but with emphasis toward business applications. Linear equations, systems of linear equations, systems of linear inequalities, elements of matrix algebra and probability. Presents some of the mathematical tools that are useful in the analysis of business and economic problems. Topics are: compound interest, annuities, differential and integral calculus...
    EUCLIDEAN GEOMETRY
    The word "geometry" comes from the Greek geometrein (geo,"earth", and "metrein, "to measure"); geometry was originally the science of measuring the land.... [a TON of stuff...]
    NUMBER THEORY
    Various topics in elementary number theory. Divisibility, congruences, quadratic reciprocity, and multiplicative functions....
    GROUP THEORY
    Zorn’s Lemma, groups, including free groups and dihedral groups. Rings including factorization, localization, rings of polynomials, and formal power series. An introduction to modules....
    RING THEORY
    Rings and field theory, including polynomial rings and field extensions....
    ADVANCED CALCULUS
    The properties of continuous mappings from N-dimensional Euclidean space to M-dimensional Euclidean space; an introduction to differential forms and vector calculus, based upon line integrals, surface integrals, and the general Stokes theorem....
    GALOIS THEORY
    The basic principles of Galois theory are introduced in this course. Topics covered are rings, polynomial rings, fields, algebraic extensions, normal extensions, and the fundamental theorem of Galois theory.
     
    Last edited: Mar 26, 2005
  5. Mar 27, 2005 #4

    matt grime

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    I got that from their "list of topics" page, and there was only the one. Perhaps a different page since the link you posted wasn't one that worked for me?

    That looks better, though why on earth zorn's lemma is in the group theory section is a mystery, mind you most of the other topics there are odd as well.
     
  6. Mar 27, 2005 #5
    its ok though, something like mathworld.wolfram.com but its not detailed enough.
     
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