Syllabus for MATHEMATICS FOR INTERNATIONAL RELATIONS

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1 Syllabus for MATHEMATICS FOR INTERNATIONAL RELATIONS Lecturers: Kirill Bukin, Nadezhda Shilova Class teachers: Pavel Zhukov, Nadezhda Shilova Course description Mathematics for international relations is a combined course taught from September through April to the first year students of the double-degree programme HSE and UoL on International Relations. No prerequisites are imposed. It consists of Calculus and Linear Algebra taught for the first 10 weeks of studies in fall and Probability Theory and Statistics taught until the end of April. Mathematics is an important part of the bachelor stage in education of the future political scientists. It has to give students skills for implementation of the mathematical knowledge and expertise. Special attention is paid to interpretation of tables and results and the appropriate way to approach statistical problems. The successful completion of that course is absolutely crucial for understanding of the Data Culture course which proceeds after the Math course. The course is taught in English. The thinking over the theoretical material presented at lectures is very important as well as a self-study at home. Teaching objectives. The objectives of the course are: to acquire the students knowledge in the field of calculus, linear algebra and statistics and to make them prepared to analyze simulated as well as real situations in the world affairs. Teaching Methods The course program consists of: - lectures, - classes (labs), - regular self-study. Assessment and grade determination Control takes the following forms: short review tests (10-15 min) in the beginning of labs; midterm exam at the end of the first module (120 min.); written exam (120 min) at the end of the second module (December); spring exam (120 min). The course grade will be determined from the following activities: short review tests (20%); lab work quality (10%);

2 fall semester midterm exam (20%); December exam (20%); spring exam (30%). Main Reading 1. Knut Sydsaeter, Peter Hammond with Arne Strom. Essential Mathematics for Economic Analysis, Pearson, 4 th edition, A.C. Chiang. Fundamental Methods of Mathematical Economics, McGraw-Hill, Newbold, P. Statistics for Business and Economics, 4 th ed. University of Illinois, 1994, or 4. Newbold, P., Carlson, W., Thorne, B. Statistics for Business and Economics (Pearson Education, 2012). Additional Reading 1. Anthony M., and Biggs N., Mathematics for Economics and Finance, Cambridge University Press, UK, Lindley, D.V., Scott, W.F. New Cambridge Statistical Tables (Cambridge: Cambridge University Press, 1995) 3. Aczel, A.D. Complete Business Statistics. (London: McGraw-Hill Higher Education, 2009) seventh edition [ISBN ]. 4. Anderson, D.R., D.J. Sweeney, T.A. Williams, J. Freeman and E. Shoesmith Statistics for Business and Economics. (South-Western Cengage Learning, 2010) eleventh edition [ISBN ]. 5. Lind, D.A., W.G. Marchal and S.A. Wathen Statistical Techniques in Business and Economics. (Boston: McGraw-Hill Higher Education, 2009) fourteenth edition [ISBN ]. 6. Wonnacott, T.H. and R.J. Wonnacott Introductory Statistics for Business and Economics. (Chichester: John Wiley & Sons, 1990) fourth edition [ISBN ] Internet resources University of London Exam papers and Examiners reports for the last three years l. 5/st104a_za15.pdf 5/st104a_zb15.pdf Course outline. Chapter 1. Mathematics (Introduction to Calculus and Linear Algebra) Part I. Basics Basic algebra, sets, functions and graphs. Part II. Differentiation The meaning of the derivative, standard derivatives. Product rule, quotient rule and chain rule. 2

3 Optimization, curve sketching, economic applications of the derivative. Part III. Integration Indefinite integrals, definite integrals, standard integrals. Substitution method, integration by parts, partial fractions. Part IV. Functions of several variables Partial differentiation, implicit partial differentiation. Critical points and their nature. Optimization, economic applications of optimization. Part V. Matrices and linear equations Vectors and matrices and operations on them. Systems of linear equations. Solving systems using row operations (case of a unique solution). Some managerial applications of linear equations. Part VI. Sequences and series Arithmetic and geometric progressions. Some financial applications of sequences and series. Chapter 2. Statistics 1. Main concepts of statistics. Sampling. Problems concerning making sense of numerical information. What is quantitative methods. Analysing relationships. Dealing with uncertainty. Probability. Forecasting. 2. Measures of central tendency. Mean, median, mode. Population mean, sample mean. Measures of dispersion: variance, standard deviation, mean absolute deviation. The population variance, the population standard deviation, the sample variance, the sample standard deviation. The range, the interquartile range. 3. Grouped data and histograms. Different kinds of data representation. Bar charts. Time plots, scatter plots. Misleading data representation. Diagrams, histograms. 4. Probability. Probability, subjective probability, conditional probability. Probability postulates. Random experiment, outcomes, events. Relative frequencies, cumulative frequencies. Bayes theorem. Discrete random variables and probability distributions. Statistical independence. 5. Continuous random variables and probability distributions. The normal distribution. Probability function. Cumulative probability function. Probability density function. Jointly distributed continuous random variables. Normal distribution and its properties. 6. Sampling and sampling distributions. Random sample. Standard error. Sample proportion. Chi-square. Degrees of freedom. 7. Interval estimation. Confidence intervals. Student s t distribution. 8. Hypothesis testing. Hypothesis. Null hypothesis. Type I errors, type II error. Significance level. Measuring the power of the test. P-value. 9. Linear correlation and regression. Correlation. Covariance. Least squares estimation. Dependent and independent variables. Standard assumptions for the linear regression model. Explanatory power of linear regression equation. Residuals. Coefficient of determination. 3

4 10. Survey sampling methods. Determining the sample size. Simple random sampling. Stratified sampling. Probability sampling. Sampling with and without replacement. Systematic sampling. Cluster sampling. Two-phase sampling. Nonprobabilistic sampling methods. Sampling errors. Distribution of hours of the Chapter 1 Topic Total Lectures Classes Self study Part I. Basics 1. Main concepts of set theory. Operations on sets Part II. Differentiation 2. The meaning of the derivative. Standard derivatives. Product rule, quotient rule, chain rule. 3. Optimization and curve sketching Economic applications of the derivatives Part III. Integration 5. Indefinite integrals, definite integrals, standard integrals. Substitution method, integration by parts, partial fractions. Part IV. Functions of several variable 6. Partial differentiation. Implicit partial differentiation. Critical points and their nature. Optimization. Part V. Matrices and linear equations 7. Vectors and matrices. Operations on them Systems of linear equations. Solving the systems using row operations. Part VI. Sequences and series 8. Arithmetic and geometric progressions. Some financial applications of sequences and series. Total: and Chapter 2 Topic Total Lectures Classes Self study 1. Main concepts of statistics Measures of central tendency Grouped data and histograms Probability Continuous random variables and probability distributions. The normal distribution. The Central limit theorem 6 Sampling and sampling distributions

5 7 Interval estimation Hypothesis testing Linear correlation and regression Survey sampling methods Total: