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STA1001 Mathematics and Statistics
This module introduces basic concepts and methods in linear algebra and calculus that are often used in business applications. Topics selected include numbers and functions, logic, matrix theory, differentiation and integration. Students are equipped with basic skills of calculus, which is the core of many mathematical disciplines such as optimization, financial mathematics, statistics, simulation etc. Students are also enabled to use mathematical methods of calculus and linear algebra for solving a range of practical problems. Applications to business management and economics are provided.
Upon completion of this module, students should be able to:
a. understand the basic concepts of number system and functions, binomial theorem and mathematical induction;
b. evaluate limits, derivatives and integrals of functions;
c. implement basic operations for vectors, matrices, determinants, and solve linear system of equations; and
d. apply techniques of linear algebra and calculus to solve a range of problems in business management and economics.
1. Preliminaries
1.1 Numbers and functions
1.2 Mathematical induction
1.3 Binomial theorem
2. Limit and continuity
2.1 Concept of limit
2.2 Concept of continuity
3. Differentiation
3.1 Differentiation and derivatives
3.2 Differentiation techniques
3.3 Higher-order derivatives
3.4 Partial differentiation
3.5 Applications
4. Integration
4.1 Definite and indefinite integrals
4.2 Integration techniques
4.3 Applications
5. Linear equations and matrix algebra
5.1 System of linear equations
5.2 Fundamental matrices operations
5.3 Determinants and inverse matrix
5.4 Solving a linear system
5.5 Applications
1. Assignments (20%)
2. Test (30%)
3. Examination (50%)
1. Fitzpatrick, P. M. (2009). Advanced Calculus (2 nd revised ed.). American Mathematical Society.
2. Lay, D. C. (2011). Linear Algebra and Its Applications (4 th ed.). Pearson.
3. Strang, G. (2016). Introduction to Linear Algebra (5 th ed.). Wellesley Cambridge Press.
4. Strang, G. (2017). Calculus (3 rd ed.). Wellesley Cambridge Press.
