FUNDAMENTALS OF MATHEMATICS AND STATISTICS
Mathematics and Statistics are the two major branches of science that find unparalleled applications in human life. Mathematical and statistical analysis are essential to many fields such as natural sciences, engineering, medicine, economics, finance, business and social sciences, especially in our computer-driven era.
The course is designed to strengthen student’s mathematics knowledge and skills so that they are equipped to pursue continued education in other quantitative fields such as data science, actuarial science, etc. Even if you are a non-mathematics or non-statistics major student, but interested to work in the field and want more targeted education in a specific area, or you need additional courses to pursue graduate study, a graduate certificate in mathematics and statistics is worth considering.
Generally, students from other disciplines who need to understand and use mathematics and statistics in their careers (e.g. finance, insurance, engineering, etc.) will find the certificate program useful and far shorter in term than a regular graduate degree. This program is intended to equip the students with some basic knowledge of mathematics and knowledge regarding the collection, organization, presentation, analysis and interpretation of numerical data. This program will also include some fundamentals of computer science and programming, that is extremely required in the field.
Syllabus
Mathematics [50 hours]
- Matrices of real numbers : Equality of matrices, Addition of matrices, multiplication of a matrix by a scalar, multiplication of matrices, transpose of a matrix and its properties, Inverse of a non singular square matrix, symmetric and skew-symmetric matrices, solution of a system of three linear equations in three variables by matrix inversion method and by sweep-out process.
- Differential Calculus: Derivative-its geometrical and physical interpretation, Evaluation of derivatives using first principle, chain rule, parametric derivative, derivative of implicit functions
- Integral Calculus: Evaluation of Improper integrals using standard integrals, integration by substitution, integration by parts.
- Ordinary Differential Equations (ODE) : Order, degree and solution of an ODE in presence of arbitrary constants, Formation of an ODE, first order ODE, solution of first order ODE using separation of variables, solution of homogeneous ODE, Solution of linear differential equations and Bernoulli’s equations.
- Basics of computer science & programming: Historical development, Computer generation, Operating system, hardware and software, Positional number system, Binary to decimal and decimal to binary, other systems like octal, hexadecimal, Machine language, Assembly language, compiler, interpreter, object program and source program, Algorithm and flow charts-their utilities and important features, application in simple problems
Statistics [50 hours]
- Collection and Presentation of data: Concepts of population and sample; Types of Statistical Data; Tabulation and diagrammatic representation of data; Frequency distribution, Cumulative frequency distribution and their graphical representation.
- Descriptive Analysis of Univariate data: Measures of Central Tendency – Mean, Median, Mode; Measures of Dispersion – Range, Mean Deviation, Standard Deviation, Quartile Deviation, Coefficient of Variation.
- Descriptive Analysis and Presentation of Bivariate data: Scatter Diagram; Simple Correlation and Regression; Rank Correlation.
- Basics of Probability: Random experiments and different types of events; Classical definition and principal theorems; Conditional Probability; Independence of Events.
- Statistics using Excel: Introduction to Spreadsheet; Presentation of Quantitative Data – Creating easy to understand charts; Analysis of quantitative data – Use of some statistical and mathematical functions.