The book that you pick up has been developed for students of first year courses in International Relations, Finance and Management. It has been designed to help you - even those who learned mathematics in high school only at the elementary level - to pass the exams in mathematics (or any other similar courses).
The book is prepared in a way that allows you to learn by yourself. Hence, great emphasis was placed on the examples that dominate in this book. They are
resolved "step by step" to make it easy to understand them.


Chapter 1. Logic
1.1. Sentences
1.2. Quantifiers

Chapter 2. Sets
2.1. Basic Concepts
2.2. Cartesian Product
2.3. The Inclusion-Exclusion Principle

Chapter 3. Relations
3.1. Describing the Relations
3.2. Properties of the Relations
3.3. Orders and Preferences
3.4. Pareto Efficiency

Chapter 4. Matrices and Vectors
4.1. Basic Concepts. Matrix Algebra
4.2. Elementary Operations
4.3. Linear Independence of Vectors and Matrix Rank
4.4. Determinants
4.5. Matrix Inverse

Chapter 5. Linear Systems
5.1. Systems of Linear Eąuations
5.2. Systems of Linear Ineąualities
5.3. Foundations of Linear Programming

Chapter 6. Basic Functions and Their Properties
6.1. Basic Concepts
6.2. Polynomials and Rational Functions
6.3. Exponential Function
6.4. Logarithmic Function

Chapter 7. Seąuences and Series
7.1. Sequences and Their Limits
7.2. Arithmetic and Geometrie Progressions
7.3. Sums and Series
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Chapter 8. Functions of One Variable
8.1. Limits
8.2. Derivatives

Chapter 9. Functions of Many Variables
9.1. Functions of Many Variables and Their Derivatives.
9.2. Local Extrema
9.3. Conditional Extrema

Chapter 10. Integral Calculus
10.1. Indefinite Integrals
10.2. Definite and Improper Integrals

Chapter 11. Differential and Difference Equations
11.1. Differential Equations
11.2. Difference Equations

Chapter 12. Applications of Calculus in Economics
12.1. Differential Calculus
12.2. Important Functions

Chapter 13. Financial Mathematics
13.1. Compound Interest, Streams of Money and IRR
13.2. Loan Repayment Schedule

Chapter 14. Probability
14.1. Basic Concepts
14.2. Random Variable
14.3. Appendix: CumulatWe Distribution of N(0, 1)