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Course Outline

 The outline for the Advanced Diploma course in Applied Mathematics include:

  1. Advanced Calculus
  2. Linear Algebra
  3. Differential Equations
  4. Numerical Analysis
  5. Probability Theory
  6. Statistics
  7. Complex Analysis
  8. Mathematical Modeling
  9. Discrete Mathematics
  10. Partial Differential Equations
  11. Optimization Theory
  12. Fourier Analysis
  13. Stochastic Processes
  14. Operations Research
  15. Graph Theory
  16. Cryptography
  17. Mathematical Logic
  18. Chaos Theory
  19. Control Theory
  20. Mathematical Physics
  21. Computational Mathematics
  22. Game Theory
  23. Topology
  24. Functional Analysis
  25. Number Theory
  26. Wavelet Theory
  27. Differential Geometry
  28. Mathematical Biology
  29. Fluid Dynamics
  30. Mathematical Finance


 

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Assessments

Attempt these 10 questions: 1. Calculate the limit of (3x^2 - 2x + 1)/(2x^2 + 5x - 3) as x approaches 1. 2. Solve the integral of sin(x)cos(x) dx. 3. Find the derivative of f(x) = x^2 ln(x). 4. Solve the differential equation dy/dx = 2x + 3. 5. Calculate the determinant of the matrix [[1, 2, 3], [4, 5, 6], [7, 8, 9]]. 6. Find the roots of the quadratic equation x^2 - 5x + 6 = 0. 7. Determine the equation of the tangent line to the curve y = x^3 - 3x^2 + 2x - 1 at the point (1, -1). 8. Evaluate the sum of the series 1/2 + 1/4 + 1/8 + 1/16 + ... 9. Find the area of the region bounded by the curves y = x^2 and y = 2x - x^2. 10. Solve the trigonometric equation 2sin(x)cos(x) = sin(x).
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Further Reading

 Here's a list of 20 recommended books for further reading in applied mathematics: "Numerical Recipes: The Art of Scientific Computing" by William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery "Introduction to Algorithms" by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein "Partial Differential Equations for Scientists and Engineers" by Stanley J. Farlow "Introduction to Probability" by Joseph K. Blitzstein and Jessica Hwang "Stochastic Processes" by Sheldon M. Ross "Linear Algebra and Its Applications" by Gilbert Strang "An Introduction to Mathematical Modeling" by Edward A. Bender and Suzanne C. Brenner "Mathematical Methods for Physics and Engineering: A Comprehensive Guide" by K. F. Riley, M. P. Hobson, and S. J. Bence "Optimization by Vector Space Methods" by David G. Luenberger "Nonlinear Dynamics and Chaos: With Applications t...
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