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
The course outline for the Preparation Course is available here:
Lecture
1, Sept. 28, 2004
Calculus: The Real numbers
Linear Algebra: Vector spaces, Linear combinations, linear dependence and
indepence
Calculus Notes 1
Linear Algebra Notes 1
Lecture 2, Oct. 5, 2004
Calculus: Cauchy sequences,
completeness
Linear Algebra: More vectorspaces
Lecture 3, Oct. 12, 2004
Calculus: Completeness of the
real numbers, sup and inf.
Linear Algebra: Existence of
a basis of a subspace, dimension.
No new notes this week.
Lecture 4, Oct. 19, 2004
Calculus: Functions,
continuity
Linear Algebra: Bases and dimension
Lecture 5, Oct. 26, 2004
Calculus: Maxima and Minima,
Compactness
Linear Algebra: The dimension formula for linear transformations
Lecture 6, Nov. 2, 2004
Calculus: Differentiable
functions
Linear Algebra: Matrices and linear maps, Gaussian reduction
Calculus Notes 5
Lecture 7, Nov. 9, 2004
Calculus: The Mean Value
Theorem for Differentiable Functions
Linear Algebra: Reduced Row Echelon Form of a Matrix
Calculus Notes 6
Lecture 8, Nov 16, 2004
Calculus: Integration
Linear Algebra: Determinants
Calculus
Notes 7
Linear Algebra Notes
No Lecture Nov 23, 2004
Lecture 9, Nov. 30, 2004
Calculus: The First
Fundamental Theorem of Calculus
Linear Algebra: More Determinants
Rules for computing determinants
Lecture 10, Dec. 7, 2004
Calculus: The Log and exp
functions, the chain rule
Linear Algebra: Computing
Determinants
Lecture 11, Dec. 14, 2004
Calculus: The Trigonometric
functions, the Gamma function
Linear Algebra: Eigenvalues
Calculus Notes 10
Linear Algebra Notes 3
Lecture 12, Dec. 21, 2004
Calculus: Infinite Series
Linear Algebra: Eigenvectors
Lecture 13, Jan. 11, 2005
Calculus: Infinite series,
Power series
Linear Algebra: Orthogonality
Lecture 14, Jan. 18, 2005
Calculus: Taylor Series
Linear Algebra: Orthogonal Bases
Lecture 15, Feb. 1, 2005
Calculus: We will finish the
notes on Power Series and the notes on Taylor Series
Linear Algebra: Orthogonal
Subspaces and Orthonormal Bases
No new notes this week
Solutions
to Homework 12 and 13
Lecture 16, Feb. 8, 2005
Calculus: More
Linear Algebra: Existence of eigenvectors for a symmetric matrix.
Lecture 17, Feb. 15, 2005
Calculus: The Complex Numbers
Linear Algebra: The Singular
Value Decomposition
Lecture 18, Feb. 22, 2005
Calculus: Complex Power
Series
Linear Algebra: The
QR-Decomposition
Calculus
Notes 16
Linear Algebra Notes
Lecture 19, Mar. 1, 2005
Calculus: Functions of
Several Variables
Linear Algebra: Orthogonal
Projections
Calculus
Notes 17
Linear Algebra Notes
Lecture 20, Mar. 8, 2005
Calculus: Approximating a
function by a linear function
Linear Algebra: One Period
Market Model
There will be no lectures
during Spring Break, Mar. 15 and Mar. 22. We will resume the course on Mar.29
Lecture 21, Mar. 29, 2005
Calculus: Vector Functions,
the Chain Rule for functions of several variables
Linear Algebra: Optimal Portfolios
Calculus
Notes 19
Linear Algebra Notes
Lecture 22, Apr. 5, 2005
Calculus: The Inverse
Function Theorem
Linear Algebra: Optimal
Portfolios with a Risk Free asset
Calculus
Notes 20
Linear Algebra Notes
Lecture 23, Apr. 12, 2005
Calculus: The Inverse Function
Theorem continued, the Implicit Function Theorem
Linear Algebra: Risk Neutral
Probabilities
Lecture 24, Apr. 19, 2005
Calculus: The Implicit
Function Theorem
Linear Algebra: The
separation theorem
No new notes this week
Lecture 25, Apr. 26, 2005
Calculus: Lagrange
Multipliers
Linear Algebra: Existence of
a Risk Neutral measure
Note: Tuesday’s Lecture
will start at 5:30pm
Lecture 26, May 3, 2005
Calculus: Finish Lagrange
Multipliers
Linear Algebra: Multi-Period
Market Models
No new Notes this week
Lecture 27, May 10, 2005
Calculus: Higher dimensional
integrals
Linear Algebra: A binary tree
market model
Calculus
Notes 23
Binary Tree Model
No Lecture May 17, 2005
Lecture 28, May 24, 2005
Calculus: Multi-dimensional integrals
Linear Algebra: Martingales
Lecture 29, May 31, 2005
Calculus: Integrating
functions whose set of discontinuities has
Linear Algebra: Martingales
Lecture 30, June 7, 2005
Calculus: Fubini’s Theorem,
Integration over
Linear Algebra: Martingales
Lecture 31, June 14, 2005
Calculus: Integration over
Jordan Domains, Change of Variables in several variables
Linear Algebra: Risk Neutral Measure in the Multi-Period Market Model
Calculus
Notes 27
Martingale
Measure in the Multi-Period Market Model 1
Lecture 32, June 21, 2005
Calculus: Change of Variables
in several variables, Polar Coordinates, Curve Integrals.
Linear Algebra: Risk Neutral Measure in the Multi-Period Market Model
Calculus: Curve and Surface Integrals
Linear Algebra: Risk Neutral Measure in the Multi-Period Market Model
Lecture 34, July 5, 2005
Calculus: Surface Integrals,
Vector Fields
Linear Algebra: Risk Neutral Measure in the Multi-Period Market Model
Martingale
Measure in the Multi-Period Market Model 2
Lecture 35, July 12, 2005
Calculus: Vector Fields, Ordinary
Differential Equations
Linear Algebra: Risk Neutral Measure in the Multi-Period Market Model
Lecture 36, July 19, 2005
Calculus: Ordinary
Differential Equations, Partial Differential Equations
Lecture 37, July 26, 2005
Calculus: Partial
Differential Equations, The Heat Equation, Fourier Transform