Financial Mathematics Preparation Course
The Financial Mathematics Preparation Course is designed to provide potential students in the Financial Mathematics Master of Science Program with the necessary mathematical background. There are no admissions criteria and the program does not lead to a degree. Successful completion of the Preparation Course is not a guarantee for admission into the Master's program.
The course meets every Tuesday 5-7pm in Eckhart 202 and runs for the entire academic year. The cost of the course is $7500.
The course outline for the Preparation Course is available here:
Lecture 1: September 30, 2003
The first Calculus lecture will cover some fundamentals of the real numbers and the notion of convergence which is fundamental in Calculus.
Homework Problems are in the Notes
The Linear Algebra part will cover definition and first properties of vectorspaces, linear combinations of vectors, linear dependence and independence. Span of a set of vectors.
Homework Problems: Fraleigh p. 18: M1-M12
Calculus Notes 1
Linear Algebra Notes
Lecture 2: October 7, 2003
Calculus: Cauchy sequences and completeness of the reals, existence of sup and inf.
Homework Problems are in the Notes
Linear Algebra: More on linear combinations, bases and dimension of vector spaces.
Homework Problems: Fraleigh p. 16: 9,10,23,25,26
Calculus Notes 2
There are no new linear algebra notes this week
Solutions to Calculus Homework 1
Lecture 3: October 14, 2003
Calculus: Functions, Continuity, the Mean
Value Theorem for continuous functions
As usual Homework Problems in the notes
Linear Algebra: Content listed for last weeks lecture
Homework Problems: Same as listed for last week
Calculus Notes 3
No new linear algebra notes
Solutions to Calculus Homework 2
Lecture 4: October 21, 2003
Calculus: Compactness, Maxima and Minima of
continuous functions.
Homework in the notes
Linear Algebra: Linear Transformations and
Matrices, Changing bases.
Fraleigh: p 49, M1-M5
Calculus Notes 4
No new Linear Algebra Notes
Solutions to
Calculus Homework 3
Lecture 5: October 28, 2003
Calculus: Differentiable functions, derivative of a function.
Linear Algebra: Matrices, Reduced Row Echelon
Form.
Fraleigh: p. 73, M6-M9
Calculus Notes 5
Linear Algebra Notes: same.
Solutions to
Homework 4
Lecture 6, November 4, 2003
Calculus: The Mean Value Theorem for differentiable functions, l'Hospital's rule
Linear Algebra: Quotient spaces. The dual
space
Homework Problems on pp. 1,2,3 in the new notes (3 problems)
Calculus Notes 6
Linear
Algebra Notes 2
Solutions to
Calculus Homework 5
Lecture 7, November 11, 2003
Calculus: Integration, Uniform continuity.
Linear Algebra: The dual space, Row and Column rank of a matrix.
Calculus Notes 7
Solutions
Calculus Homework 6
Lecture 8, November 18, 2003
Calculus: More on integration, the
fundamental theorem of Calculus.
Linear Algebra: The dual space continued.
Calculus Notes 8
Solutions to Calculus
Homework 7
Lecture 9, November 25, 2003
Calculus: Log and exp functions
Linear Algebra: The dual space conclusion, application to market models
Lecture 10, December 9, 2003
Calculus: Trigonometric functions, improper
integrals, the Gamma function
Linear Algebra: Probability, Expected return, Variance.
Calculus Notes 10
Market Model 2
Lecture 11, December 16, 2003
Calculus: Infinite series, convergence tests
Linear Algebra: Portfolio optimization
Calculus Notes 11
Market Model 3
Lecture 12, January 6, 2004
Calculus: Power series and functions defined
by power series.
Linear Algebra: Portfolio optimization with a risk free asset.
The notes have been updated, please download the new set
Calculus Notes 12
Market Model 4
Lecture 13, January 13, 2004
Calculus::
Linear Algebra: Optimal Portfolios with a risk free asset.
Calculus Notes 13
Market Model 5
Lecture 14, January 20, 2004
Calculus: Remainder terms in
Linear Algebra: Example of portfolio optimization
Lecture 15, January 27, 2004
Calculus: The Complex number system
Linear Algebra: Determinants
Calculus Notes 15
Determinants
Lecture 16, February 3, 2004
Calculus: Complex power series and functions
of a complex variable
Linear Algebra: More determinants
Lecture 17, February 10, 2004
Calculus: Functions of several variables,
directional and partial derivatives.
Linear Algebra: Eigenvalues and eigenvectors
Lecture 18, February 17, 2004
Calculus: Vector Functions, Approximation by
Linear Functions
Linear Algebra: Diagonalization
Lecture 19, February 24, 2004
Calculus: The Chain Rule for Vector Functions
Linear Algebra: Diagonalization and Orthogonality
Lecture 20, March 2, 2004
Calculus: The Inverse Function Theorem
Linear Algebra: Self-adjoint operators and orthogonality
Lecture 21, March 9, 2004
Calculus: The Inverse Function Theorem continued
Lecture 22, March 30, 2004
Calculus: The Implicit Function Theorem
Linear Algebra: Orthogonal Matrices
Lecture 23, April 6, 2004
Calculus: Lagrange Multipliers and
constrained optimization
Linear Algebra: Principal Component Analysis
Lecture 24, April 13, 2004
Calculus: Multiple integrals
Linear Algebra: Risk Neutral probabilities
Calculus Notes 24
Principal Component Analysis
Risk Neutral Probabilities
Lecture 25, April 20, 2004
Calculus: Multidimensional integration
Linear Algebra: The Separation Theorem and Risk Neutral Probabilities
Lecture 26, April 27, 2004
Calculus: Integration of a function whose
discontinuities has
Linear Algebra: Risk and Return
Lecture 27, May 4, 2004
Calculus: Fubini’s Theorem
Linear Algebra: Risk and Return continued
Lecture 28, May 11, 2004
Calculus: Integration over
Linear Algebra: Multi-Period Market Model
Calculus Notes 28
Multi-Period Market Model
Lecture 29, May 18, 2004
Calculus: Change of Variables in
multi-variable integrals
Linear Algebra: Multi-Period Market Model, Information Structures
Lecture 30, May 25, 2004
Calculus: Curve integrals
Linear Algebra: Conditional Expectation and Martingales
Calculus Notes
30
Martingales
Lecture 31, June 8, 2004
Calculus: Surface integrals
Linear Algebra: Binomial Trees
Calculus Notes 31
Binomial Tree Model
Lecture 32, June 15, 2004
Calculus: Vector fields
Linear Algebra: Binomial Tree Model, Martingale measure
Lecture 33, June 22, 2004
Calculus: Ordinary Differential Equations
Linear Algebra: Martingale measure
Lecture 34, June 29, 2004
Calculus: Calculus of Variations
Linear Algebra: Martingale Measure
Lecture 35, July 6, 2004
Calculus: Partial Differential Equations 1
Linear Algebra: Completeness in a Multi-Period Market
Calculus Notes 35
Martingale Measure in a Multi-Period Market
Lecture 36, July 13, 2004
Calculus: The Fourier Transform
Linear Algebra: Local Markets
Calculus Notes 36
Local Markets
Lecture 37, July 20, 2004
Calculus: The
Linear Algebra: Martingale Measure
Calculus Notes 37
Martingale Measures
Lecture 38, July 27, 2004 Last Lecture
Calculus: The Heat Equation with Boundary
Conditions
Linear Algebra: Martingale Measure