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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

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!