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yik-boh
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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 CriterionSequences and Series of Functions
-Pointwise Convergence
-Uniform Convergence
-Properties Preserved by Uniform Convergence
- Definition of Metric and Metric Space, Euclidean Metric, Schwarz and Triangle InequalityBook being used:
Introduction to Real Analysis by William F. Trench
A First Course in Real Analysis by M.H. Protter and C.B. MorreyMath 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 StewartI 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!
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 CriterionSequences and Series of Functions
-Pointwise Convergence
-Uniform Convergence
-Properties Preserved by Uniform Convergence
- Definition of Metric and Metric Space, Euclidean Metric, Schwarz and Triangle InequalityBook being used:
Introduction to Real Analysis by William F. Trench
A First Course in Real Analysis by M.H. Protter and C.B. MorreyMath 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 StewartI 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!
