MDAE Summer Program in Math and Statistics - Syllabus
Course Curriculum

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Math

Students will learn concepts of mathematics that are most useful for understanding higher-level (i.e., quantitative aspects of) economics and finance.

These concepts are as follows –

1) Functions, Limits and Continuity
a) Introduction to Functions
b) Some common functions – 1/x, x^n, ln x, e^x, step function, saw-tooth function
c) Graphing functions
d) Limits (concept, left-hand, right-hand, etc)
e) Continuity
f) Concept of Asymptotes – Horizontal, Vertical and Slant with examples and how to find them

2) Differentiation
a) Concept of the derivative … as rate of change, as slope of tangent, etc
b) Simple rules to find derivatives explained conceptually (product, chain, etc)
c) Application of the rules to find derivatives
d) Implicit derivatives
e) Derivatives of higher order
f) Concept of partial derivatives

3) Application of derivatives
a) Increasing, decreasing
b) Maxima minima
c) Convexity, concavity

4) Anti-derivatives
a) Concept (Riemann), definition and relation to derivatives (Fundamental Theorem)
b) Common methods of integration – substitution, partial fractions and parts
c) Definite integrals and Area Under the Curve

5) Optimization
a) Level set of f (x, y) – convex level set of a quasi-concave function
b) Unconstrained Optimization in two variables
c) Constrained Optimization in two variables – Lagrangian Mulitpliers

6) Linear Algebra
a) Vector Space – spanning of R2 and R3, linear independence, basis, and rank
b) System of linear equations Ax = b – solve by substitution
c) Matrices – (+, -, *, / operations), elementary row and column operations, inverse, rank
d) Solve Ax = b using Cramer’s Rule and Gauss elimination method

7) Basic Principles of Counting
a) Fundamental Theorem of Counting
b) Permutations and Combinations
c) Inclusion-Exclusion Principle

Statistics

Students will learn concepts of statistics that are most useful for understanding higher-level (i.e., quantitative aspects of) economics and finance. These concepts are as follows:

1) Random variables

  1. Random variables and their types
  2. Discrete distributions: Binomial, Poisson
  3. Continuous distributions: Normal
  4. Cumulative Distribution function (cdf), probability mass function (pmf), probability distribution function(pdf).
  5. Expectation and Variance of Random variables
  6. Sampling distribution of sample means
  7. Mean, Median, Skewness and Kurtosis

2) Jointly Distributed Random Variables

  1. Jointly distributed random variables and their types
  2. Marginal density – Conditional probability
  3. Conditional expectation (mean) and conditional variance
  4. Covariance, Correlation and Statistical independence.

3) Elements of Hypothesis Testing

  1. Elements of hypothesis testing
  2. Standard Normal distribution
  3. Testing hypothesis about the mean when the population variance is known
  4. Confidence intervals
  5. Law of Large Numbers, Discrete distributions: Binomial, Poisson
  6. Chi square distribution – comparing sample variance with that of the population
  7. Students t- distribution when the sample size is small
  8. Size and power of a test

Duration & Structure – Blended Learning Model with self paced recorded videos, virtual live classes as well as in-room training. There will be 48 hours of training (24 hours per course)

Course Dates – 7th May to 8th June (Tentative)

Who can apply? Students in their first, second or third year of graduation – Students must have secured a minimum 50% in their 12th standard. Students appearing in 12th grade can also apply for this course.

Venue –  Meghnad Desai Academy, 12th Floor, Centre 1 Building, Cuffe Parade, Mumbai – 40005

Fees – Rs. 24,000 plus applicable taxes

For more information, please write to info@meghnaddesaiacademy.org or call 022 60126001

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