I'm a college student and I'm taking 12 units of math now. I'm having quite a hard time on some topics so I really want to know how should I study for these math topics. Can you also give some other references that I can use? (like the MIT Courseware, Harvard Online Courses, etc.) Here are the list of topics under my math classes: Math 185 - Modern Geometry Klein's idea of Geometry Mobius Geometry Hyperbolic Geometry Elliptic Geometry Absolute Geometry Real Projective Plane, Multidimensional projective Plane Universal Geometry Axiom Systems: Hilbert's and Bachmann's Books being used: Modern Geometries The Analytic Approach by Micheal Henle Math 171 - Advanced Calculus I (It includes Calculus topics but not the computation part but more on proving and analysis) The Real Number System -Supremum and Infimum of a Set -Completeness Axiom -The Archimedean Property -Density of the Rationals and Irrationals -Extended Real Number System The Real Line -Some Set Theory -Open and Closed Sets -Open Coverings, Heine-Borel Theorem -The Bolzano-Weierstrass Theorem Functions and Limits -Epsilon-delta Definition of Limits -Limit Inferior and Limit Superior Continuity -Definition of Continuity -Bounded Functions, Boundedness Theorem -Extreme Value Theorem -Intermediate Value Theorem -Uniform Continuity, Uniform Continuity Theorem Integral Calculus -Definitions -Integral as the Area under a Curve -Upper and Lower Integrals -Existence of the Integral -Function of Bounded Variation -Riemann-Stieltjes Integral Sequences of Real Numbers -Limit of a Sequence, Convergence and Divergence -Bounded and Monotonic Sequences -Sequences of Functional Values -A Useful Limit Theorem -Limit Superior and Limit Inferior -Cauchy's Convergence Criterion Sequences and Series of Functions -Pointwise Convergence -Uniform Convergence -Properties Preserved by Uniform Convergence - Definition of Metric and Metric Space, Euclidean Metric, Schwarz and Triangle Inequality Book being used: Introduction to Real Analysis by William F. Trench A First Course in Real Analysis by M.H. Protter and C.B. Morrey Math 101 - Mathematical Analysis III (This one is heavy in Calculus. More on Vector Calculus) Vectors and the Geometry of Space -Vectors -Dot Product -Cross Product -Equations of Lines and Planes -Cylinders and Quadric Surfaces Vector Functions -Vector Functions and Space Curves -Derivatives and Integrals of Vector Functions -Arc Length and Curvature -Motion in Space: Velocity and Acceleration Partial Derivatives -Partial Derivatives -Tangent Planes and Linear Approximation -Directional Derivatives and The Gradient Vector -Lagrange Multipliers Multiple Integrals -Review of Double and Triple Intergals -Triple Integrals in Cylindrical Coordinates -Triple Integrals in Spherical Coordinates -Change of Variables in Multiple Integrals Vector Calculus -Vector Fields -Line Integrals -The Fundamental Theorem for Line Integrals -Green's Theorem -Curl and Divergence -Parametric Surfaces and their Areas -Surface Integrals -Stokes' Theorem -The Divergence Theorem Book being used: Stewart's Calculus Early Transcendentals by James Stewart I still another Math but I misplaced the class syllabus and I'm going to look for it first. I'll post it here when I find it. I'm really having a hard time in making proofs especially in Math 171. I got a 18/80 on our first long exam. :| I really want to do better in the remaining exams so I hope you can help me. Thanks!