2. Section 2

CBR/STAT04 - Vector Analysis

Multiplication of vectors by scalars and addition of vectors
Geometry with vectors
Geometry
Scalar product
Applications to metric geometry
Vector product and scalar triple product
Geometry with Cartesian co-ordinates
Statics with vectors
Vector valued functions of scalar variables
Differential operators
Integral transformation

CBR/STAT05 - Mathematical Modeling

The probability paradigm
The binomial model and random variables
Continuous random variables and the Gaussian model
Statistics
The Poisson model
Modeling random signals
References

CBR/STAT07 - Differential Equations

Elementary differential equations
Equations of first order and first degree
Trajectories
Linear equations with constant coefficients
Homogeneous linear equations and Cauchy-Euler equations
Equations of the first order but not of the first degree and singular solutions
Extraneous loci
Ordinary simultaneous differential equations
Number integration
Picard's interactive methods
Existence and uniqueness theorems
Independence of solutions of linear differential equations
Wronshian and its equations
Exact differential equations and equations of special forms
Linear equations of second order
Simultaneous equations of the form dx/R = dy/Q=dz/R
Total differential equations
Riccati's equations
Integration in series
Series solutions of linear differential equations
Legendre polynomials and functions
Legendre functions of second kind
Bessel functions
Hermite polynomials
Laguerre polynomials
Hyper-geometric functions
Partial differential equations' Linear partial differential equations of order one
Non-linear partial differential equations with constant coefficients
Partial differential equations of order two with available coefficients
Monge's methods
References

CBR/STAT08 - Sequences and Series

Sets and statements
The real number
Neighborhoods and limit points of a set
Sequences
Infinite series with positive terms
Infinite series with positive and negative terms
Real functions-limit and continuity functions
Real functions - the derivative
Reimann integrability

CBR/STAT09 - Linear Algebra

A system of vectors
Matrices
Elementary row operations
An introduction to determinants
Vector spaces
Linear mappings
Matrices from linear mappings
Eigenvalues, Eigenvectors and diagonalization
Euclidean spaces
Quadratic forms

Electives 3: Select one course from -

FIN05 - Taxation

Introduction
Tools of positive analysis and normative analysis
Public goods
Externalities
Political economy
Income redistribution - conceptual issues
Expenditure programs for the poor
Social insurance - social security and unemployment insurance and health care
Cost benefit analysis
Taxation and income distribution
Taxation efficiency
Efficient and equitable taxation
The personal income tax
Personal taxation and behavior
The corporate tax
Deficit finance
Taxes on consumption and wealth
Public finance in federal system

FIN06 - Monetary and Currency Systems

Institutions
Money and its payment system
Credit and the financial systems
Financial markets
Reserve banks and reserve systems
Commercial banks
Development banks
Non bank financial intermediaries
Unregulated credit markets
Money theory
Demand for money
Money and prices
Money, interest and income
Inflation
Theory of money supply
The supply of credit and its allocation
Interest rates
Money policy
Goals, targets and indicators
Instruments of control
Monetary policy
Credit policy of reserve banks
References

FIN07 - Fundamentals of Financial Management

Introduction
The financial markets and interest rates
Understanding financial statements and cash flows
Evaluating a firm's financial performance
Financial forecasting, planning and budgeting
The time value of money
Valuation and characteristics of bonds
Valuation and characteristics of stock
The meaning and measurement of risk and return
Capital-budgeting techniques and practice
Cash flows and other topics in capital budgeting
Determining the financial mix
Dividend policy and internal financing
Introduction to working-capital management
Liquid asset management
International business finance

FIN08 - Econometrics

Introduction
Brief overview of the statistical applications to econometrics
Multi-collinearity - correlated regressions
Hetero-scedasticity - error-variance is non-constant
Auto-correlation - error terms are correlated
Econometric modeling - model specification and diagnostic testing
non-linear regression models
Qualitative response regression models
Panel data regression models
Dynamic econometric model - auto-regressive and distributed lag model
Simultaneous equation problem
The identification problem
Simultaneous equation methods
Time series econometrics - basic concepts and forecasting

3. Section 3

CBR/FIN05 - Complex Analysis

Complex analysis
Geometrical representation of complex numbers
Bilinear transformations
Topological considerations
Analytic functions
Infinite series
Power series
Conformal mapping
Complex integration
Cauchy theory
Singular points
Calculus of residues
Uniform convergence infinite products
Analytic continuation
Entire functions

CBR/FIN06 - Logic and Group Theory

Introduction
Argument structure
Argument evaluation
Prepositional logic
The prepositional calculus
The logic of categorical statements
Predicate logic
The predicate calculus
Introduction to fallacies
The probability calculus
Further developments in formal logic

CBR/STAT14 - Matrices

Fundamental concepts
Algebra of matrices
Rank of a matrix
Vector spaces of n-tupelos and their transformations
Systems of linear equations
Quadratic forms and congruence of matrices
Quadratic forms in the real field
Hermitian matrices and forms
Orthogonal matrices - unitary matrices
Characteristic roots and characteristic vectors of a matrix
Orthogonal and unitary reductions of quadratic forms
Similarity of matrices
References

CBR/FIN07 - Fourier Analysis

The Fourier method
Orthogonal sets and Fourier series
Convergence of Fourier series
Boundary value problem
Sturm-Liouville problems and applications
Legendre polynomials and applications
Verification of solutions and uniqueness
References

CBR/FIN08 - Financial Derivatives

Financial derivatives markets
An overview
Options
Convertible securities
Warrants
Futures
Currency futures and options
Forward and future contracts and portfolio risk
Swap markets
Swaps - asset and liability management
Modern banking and over-the-counter derivatives markets
Financial derivatives
Risk control and accountability
Managing derivatives risks - an integrated approach
Creating risk-management value chain

CBR/FIN09 - Real Analysis (sequences and series)

CBR/FIN10 - Optimization

Problem solving with mathematical models
Deterministic optimization models in operations research
Improving search
Linear programming models
Simplex search for linear programming
Interior point methods for linear programming
Duality and sensitivity in linear programming
Multi-objective optimization and goal programming
Shortest path and discrete dynamic programming
Network flows
Discrete optimization models and methods
constrained and unconstrained non-linear programming

Electives 4: Select one course from -

FIN11 - International Economics

The basic theory using demand and supply
General trade - comparative advantage and factor proportions
Gains and loses in trade
Alternative theories of trade
Growth and trade
The basic analysis of tariffs
Non-tariff barriers to imports
Arguments for and against protection
Pushing exports
Trade blocs and trade blocks
Trade and environment
Trade policies for developing and transition countries
Multinationals and migration - international factor movements
Payments among nations
The foreign exchange and international financial investment
What determines exchange rates
Government polices toward foreign exchange market
International lending and financial crises
Functioning of open macro-economy
International and external balance with fixed exchange rates
Floating exchange rates and internal balance
National and global floating rates

FIN12 - Strategic Management

Basic concepts of strategic management
Corporate governance and social responsibility
Environmental scanning and industry analysis
Internal scanning organizational analysis
Strategy formation - situation analysis and business strategy, corporate strategy, functional strategy and strategic choice
Strategy implementation - organizing for action, staffing and leading
Evaluation and control
Case studies

FIN13 - Financial Management

Introduction
Interpreting financial statements
Evaluating financial performance
Financial forecasting
Managing growth
Financial instruments and markets
The financial decision
Discounted cash flow techniques
Risk analysis in investment decisions
Business valuation and corporate restructuring