This github profile is used to post computational materials related to subjects studied in BSc Applied Mathematics as an undergraduate and post graduate. Materials related to certification courses are also included.
Programming languages implemented: 
Applied Mathematics Undergraduate and Postgraduate:
| Theme | Description |
|---|---|
| Mathematical Statistics in R | Covering: Limiting Distributions ; Statistics and Sampling Distributions ; Point Estimation, Sufficiency and Completeness, Interval Estimation ; Tests of Hypotheses |
| Multivariate Mathematical Statistics in SAS | Covering: Multivariate Distributions ; Simple and Multiple Linear Regression ; One-way ANOVA and ANCOVA ; Poisson and Logistic Regression |
| Numerical Analysis in Python | Covering: Direct methods for solving linear systems ; Iterative techniques in matrix algebra ; Numerical solution of eigenvalue problems, the power method ; Numerical methods for initial and boundary value problems for ODE's ; Numerical solution of nonlinear systems of equations. |
| Financial Engineering 1 in Microsoft Excel | 1 . Asset valuations. - Mean-Variance Portfolio Theory. - Asset pricing models [CAPM]. - Single and multifactor models for investment returns. 2 . Theories of financial market behavior. - Rational choice theory [Utility theory and properties]. - Stochastic Dominance. - Rational Expectation theory [EMH] and Behavioural Economics. 3 . Measures of investment risk. 4 . Stochastic interest rate models. |
| Financial Engineering 2 in Python and Microsoft Excel | 1. Arbitrage, replicating portfolios, the single step binomial model Pricing of forwards options and implementing delta hedging with the single step binomial model. 2. n-Step Binomial Trees Pricing of forwards options and implementing delta hedging with the n-step binomial model. 3. Brownian Motion and Stochastic Calculus Brownian Motion, Stochastic Calculus and Ito Calculus, Stochastic Differential Equations, Stochastic PDE's and Feynman Kac Method 4. Continuous Models: Black-Scholes Theory Log-Normal Stock model, Self-financing Strategies, Solving and modelling Black-Scholes PDE, Risk Neutral Strategies, Hedging and the Greeks. 5. The Term Structure of Interest Rates and Bonds Interest Rates, Forward Rates, Yield Curves, Market Price of Risk, Bond Price Models, Short Rate Models. 6. Credit Risk The Merton Model and the Jarrow, Landow, Turnbull Model. Spesific computational topics explored in Microsoft Excel: - Calibrating the (discrete) binomial model. We use the Cox-Ross-Rubenstein approach for our binomial tree model. - Using of market data to find implied volatilities. - Using implied volatilities together with the Black-Scholes formulae, binomial trees and spreadsheets to price various derivative securities. |
Certification Courses:
| Course Title | Description |
|---|---|
| SQL for Data Analysis with Microsoft SQL Server | To query databases with SQL ; Installing and working with Microsoft SQL Server 2019 and SQL Server Management Studio ; Use SQL to apply complex criteria and transformations to database data ; Master SQL functions for sophisticated data manipulation ; Leverage an understanding of relational database design to link together data stored across multiple tables ; Use aggregate queries to produce summarized views and analysis |
| Advanced Microsoft SQL Server for Data Analysis | Window Functions ; Correlated Subqueries ; Advanced filtering with EXISTS and NOT EXISTS ; Flattening data with PIVOT ; Generating data series with Recursive CTEs ; Leveraging CTEs and temporary tables to break complex processes into manageable steps ; Defining and manipulating tables with DDL and DML commands ; Designing lookup tables to simplify redundant analysis ; SQL optimization techniques including indexes ; Procedural programming techniques like variables and IF statements ; Defining your own SQL functions ; Creating stored procedures for flexible, repeatable analysis. |
| Advanced PostgreSQL for Data Science and Time Series Analysis | Basics of time series data ; Writing time series data ; Querying time series data ; Installing PostgreSQL and working with the pgAdmin IDE ; Evaluating query performance ; Joining time series ; Denormalizing time series ; Indexing data ; Querying a partitioned table ; Functions for time series ; Calculating aggregates over windows ; Calculating moving averages ; Forecasting with linear regression |
| Standard Bank - Data Science Virtual Experience Program with Forage | Cleaning data in SQL ; Working with the CRISP-DM methodology ; Machine Learning and Automated Machine Learning in Python ; Performing Exploratory Data Analysis as well as automated EDA in Python ; Drafting a presentation in Microsoft PowerPoint and Video presentation outlining the results of the project. |