## SHEB104 Quantitative Methods for Business

### Annotation:

This introductory unit provides an understanding of the basic mathematical methods required for the study of business and finance related problems. This course satisfies the mathematics competency requirements for a first year student in business.

This unit aims to:

• Develop students’ mathematical skills to structure mathematically business and financial concepts.

• Provide them with the necessary tools to address business and financial problems.

• Enhance the ability of the students’ to relate the specific mathematical solutions to real business and financial context.

### Lecturers:

**Dr. Petros Golitsis**

**Сава Гроздев**

**Assist. Prof. Ekatherina Tzvetanova-Georgieva, PhD**

### Course Description:

**Competencies:**

Students who complete this course:

1) will know:

• Compute the breakeven point and demonstrate an understanding of the breakeven point analysis

• Model sample regression functions with the usage of matrix algebra.

2) will be able to:

• Apply the simple supply and demand functions and find equilibrium points.

• Undertake basic matrix operations, including inversion, and apply them to input-output analysis.

• Differentiate simple functions and apply the methods to economic analysis including marginal cost, revenue and profit, and elasticity.

• Undertake financial calculations involving compound interest, including net present value.

**Prerequisites:**

Students are required to have the following knowledge and/or skills:

• No preliminary requirements

**Types:**

Full-time Programmes

**Types of Courses:**

Lecture

**Language of teaching:**

English

### Topics:

- Introduction to quantitative techniques. The mathematical preliminaries Relations and functions, Dependent and independent variables, Functions with one or more independent variables, References: • [B] Essential mathematics for Economics and business, Wiley, Chapters 1, 2 and 3. Further reading: Haeussler, E.F., Paul, R.S. and Wood, R.J, Introductory Mathematical Analysis, Pearson, Chapters 1, 2 and 4.
- Mathematical Preliminaries. The equilibrium concept and the break-even analysis Graphs of linear functions, The slope and the intercept, Supply and Demand Analysis, References: • [B] Essential mathematics for Economics and business, Wiley, Chapters, 2 and 3. Further reading: Haeussler, E.F, Paul, R.S. and Wood, R.J., Introductory Mathematical Analysis, Pearson, Chapters 2 and 4.
- Mathematical Preliminaries. The equilibrium concept and the break-even analysis Break-Even Point, Introduction to Excel. References: • [B] Essential mathematics for Economics and business, Wiley, Chapters, 2 and 3. Further reading: Haeussler, E.F, Paul, R.S. and Wood, R.J., Introductory Mathematical Analysis, Pearson, Chapters 2 and 4.
- Linear Algebra Basic Matrix Operations, The Matrix Form of a System of Linear Equations, The Inverse Matrix. References: • [B], Essential mathematics for Economics and business, Wiley, chapter 9. Further reading: Haeussler, E.F, Paul, R.S. and Wood, R.J., Introductory Mathematical Analysis, Pearson, Chapter 6.
- Linear Algebra Crammer’s Rule, Gaussian Elimination. References: • [B], Essential mathematics for Economics and business, Wiley, chapter 9. Further reading: Haeussler, E.F, Paul, R.S. and Wood, R.J., Introductory Mathematical Analysis, Pearson, Chapter 6.
- Linear Algebra Matrix Operations, Excel for Linear Algebra and using matrices for regression purposes. Introduction to sample regression function. References: • [B], Essential mathematics for Economics and business, Wiley, chapter 9. Further reading: Haeussler, E.F, Paul, R.S. and Wood, R.J., Introductory Mathematical Analysis, Pearson, Chapter 6.
- Differentiation and Applications The derivative of a function, Rules of differentiation, Marginal Revenue, Marginal Cost, Marginal Profit, Elasticity. References: • [B], Essential mathematics for Economics and business, Wiley, chapter 6. Further reading: Haeussler, E.F, Paul, R.S. and Wood, R.J., Introductory Mathematical Analysis, Pearson, Chapters 12, 13 and 15.
- Mathematics of Finance Simple interest, Compound Interest, Present Value, Future Value, Monthly Compounding, Excel for financial mathematics. References: • [B], Essential mathematics for Economics and business, Wiley, chapter 5. Further reading: • Haeussler, E.F, Paul, R.S. and Wood, R.J., Introductory Mathematical Analysis, Pearson, Chapter 8.
- Mathematics of Finance Annuities, Monthly Compounding, Excel for financial mathematics. References: • [B], Essential mathematics for Economics and business, Wiley, Chapter 5 Further reading: Haeussler, E.F, Paul, R.S. and Wood, R.J., Introductory Mathematical Analysis, Pearson, Chapter 9.
- Perpetuities, Monthly Compounding, Excel for financial mathematics. References: • [B], Essential mathematics for Economics and business, Wiley, Chapter 5 Further reading: Haeussler, E.F, Paul, R.S. and Wood, R.J., Introductory Mathematical Analysis, Pearson, Chapter 9.
- Revision