Syllabus

Országok listájaHungaryBudapesti Corvinus EgyetemGazdálkodástudományi KarNemzetközi gazdálkodás (angol nyelven)Mathematics2JegyzetekSyllabus

SYLLABUS

Mathematics II
BA in International Business Year 1 2007/2008
Course code: Department: Name of department: Mathematics Location of department: Sóház building Phone number: 482-7439 webpage: http://web.uni-corvinus.hu/math Course unit leader: Name, title: Tallos, Peter, Professor - Department Head Office number: S206 Phone number: 482-7432 e-mail address: tallos@uni-corvinus.hu Name, title: Puskás Csaba, Associate Professor Office number: S208/b Phone number: 482-7434 e-mail address: puskas@uni-corvinus.hu e.g. Monday 9.00-10.30 You are welcome to drop in at this time but individual appointments can be made in advance for a time that better suits your convenience. Status: Contact hours: Credits: Prerequisites Venue: Time: Foundation of mathematics I. NG-A - 4MA13NAK15B E.3.326 E.3.395 17.50 Core 1+1

Spring Term

Tutor(s):

Office hours:

Tuesday 8.00-9.20, Wednesday 16.30

Aims and objectives The aim of this course is the preparation of students to have a better understanding of

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statistical inference. Without some formalism in probability the student can not appreciate the true interpretation of data analysis through modern statistical methods. The discipline of probability provides the transition between descriptive statistics and inferential methods. To understand some basic concepts in probability theory we use integral calculus and elements of theory of series. Learning outcomes

· · ·

Understanding the role of quantitative methods applied in processing data. Knowledge of the mathematical methods used in the applications. Understanding the evaluation of chance outcomes of processes, statistical experiments.

Course description This second course of mathematics is going to make the mathematical foundation of statistics, therefore it covers elementary probability theory. Some of the concepts in probability theory assume the knowledge of integral calculus and the elements of the theory of numerical and power series, hence these topics will be studied first. We extend the addition of numbers and functions of infinitely many terms. We introduce the concept of Riemann integral and improper integral and learn some methods for integration. We introduce the concept of statistical experiment, and measure the chance of the outcomes of the events. Introducing random variable we make applicable the tools of calculus. We study the most often occurring discrete and continuous probability distributions, their important characteristics like the expected value (mean) and variance and standard deviation. We also study joint random variables, their covariance and correlation. In some cases when the distribution of a random variable is unknown we can only give an estimation on the probability of some events using the Chebishev's inequality and the Bernoulli's theorem. Eventually we deal with the sample distribution of means and learn about the central limit theorem. Course schedule Month 02 02 Day Topic/Content 05 06 Series, power series, the Taylor series of the exponential function. (web) Sum of series, criteria of convergence, radius of convergence. (web) 2

02

12

Antiderivative, indefinite integral, definite integral, the Fundamental Theorem of Calculus. (B1: CH 9.1-9.3 + web) Finding the indefinite integral of some elementary functions. (web) Integration by parts and by substitution, improper integral. (B1: CH 9.5-9.7 + web)

02 02

13 19

02

20

Application of the integration methods. Integration of rational functions. (web)

02 02 03

26 27 04

Double integral on rectangular regions. (web) Summary of integral calculus. Experiments, sample space, algebra of events, probability space. (B2: CH 2.1 -2.2) Exercises (B2 pp.39-40, 47-48) Elements of combinatorics. (B2 CH 2.3 Finite and countable sample spaces, finding the probability of events using combinatorics. (B2 CH 2.4 2.5)

03 03

05 11

03 03

12 18

Exercises (B2 pp.55-58) Conditional probability. Multiplicative rules (B2: CH 2.6 -2.7) Exercises (B2 pp. 65-67)

03

19

Theorem of total probability, Bayes' rule. (B2 CH: 2.8) Exercises (B2 pp. 72-75)

04

01

Random variables, Probability distribution, cumulative distribution function, density function. (B2 CH: 3.1-3.3)

04 04

02 08

Exercises (B2 pp. 88-91) Special discrete distributions. (B2 CH: 5.1 -5.6) Exercises (B2 pp. 150-152, 157 -158, 165-169)

04

09

Some continuous probability distributions. (B2 CH: 6.1-6.4, 6.6-6.7) Exercises (B2 pp.185-187, 205-208)

04

15

Transformations of random variables. The concept of expected value, standard deviation and variance of random variable. (B2 CH: 4.1-4.3) Exercises (B2 pp.113 115, 122, 134 - 138)

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04

16

The expected value and standard deviation of some special distributions. (B2 CH: 5.1-5.6, 6.1-6.4, 6.6-6.7 revisited)

04

22

Joint probability distributions, marginal distributions. The independence of random variables. (B2 CH: 3.4)

04 04

23 29

Exercises (B2 pp. 101-105) Theorems on the expected value and standard deviation. Covariance and correlation of random variables. (B2 CH: 4.2-4.4 +web)

04 05 05 05 05

30 06 07 13 14

Chebyshev's theorem. Bernoulli's theorem. Exercises (B2 pp. 134-138) Normal distribution and the central limit theorem. (B2. CH: 8.4 +web) Exercises (B2 pp. 251 - 253 Review session problem solving.

Preparation of final exam.

Methodology We are not going to sharply separate the lectures and seminars and try immediately apply the theoretical results in problem solving, therefore the participation is expected. For each class meeting some homework will be assigned. The solution of problems at home will be checked on quizzes. The collective work on the homework problems is allowed, but the reproduction on quizzes must be individual work.

Assignments In the above schedule the week -by -week tasks are given and also given the set of exercises to be solved, further specification will be given in classes. Assessment and grading During the semester 4 short (10 minutes) quizzes will be given for 10 points each. Furthermore the students have to take a midterm and a final exam, where 35-35 points can be collected. The result of the weakest quiz is dropped. From each unit 40% of the available

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points must be collected to pass the course, without repeating exam. Grades will be given according to the following pattern: Quizzes: Midterm exam: Final exam: 30% 35% 35% 100%

Grading, assuming that from each component at least 40% of the available points is collected: 0-40% fail 41-55% pass 56-70% satisfactory 71-85% good 85-100% excellent

Course policies The attendance of classes is required. No make-up classes! Without acceptable reason (like serious illness) missed quizzes and exams result in zero point! Academic dishonesty, like cooperation on exams induce disqualification. Compulsory readings B1: K. Sidsaeter P. Hammond: Essential Mathematics for Economic Analysis, Myers Ye: Probability & Statistics for Engineers & Scientists, B2: Walpole Myers

http:/web.uni-corvinus.hu/puskas Mathematics II.

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