Project MetaMath outlines a probability theory and mathematical statistics course offered at Tver State University. The course is offered over two semesters for a total of 9 credits. It includes lectures, laboratory work, seminars, course projects each semester, and exams. The goal of the course is to present basic information about probability models that account for random factors. Upon completing the course, students should have mastered key probability and statistics concepts and techniques. The course also discusses modernizing elements like pre-testing students and incorporating online homework assignments.

1. Project MetaMath
Probability theory and mathematical statistics in Tver State University

2. Probability theory and mathematical statistics
in TSU
Duration: 2 semesters (37 weeks)
Preferred year/semester: 2, 3 / 4, 5
Prerequisite Courses: Linear algebra, Mathematical analysis,
Differential Equations
Amount of credits – 9 (1 ≡36 hours)
Forms of control: modules, course project (each semester), exam
(each semester)

3. Probability theory and mathematical statistics
in TSU
Classroom load:
• lectures – 74 hours,
• laboratory work / seminars – 74 hours,
• exam preparation – 27 hours.
Homework – necessary.
Assessment – 2-5
Methodological materials, lectures, guidelines for implementation of
course work in electronic form in the public domain.

4. Probability theory and mathematical statistics
in TSU
Discipline = 100 marks: work in the semester – 60, exam – 40
The exam includes:
1. two questions (20)
2. list of basic knowledge (theorems, definitions, formulas)
(10)
3. solution of task (10)
Exam preparation – 27 hours.
Assessment (2-5):
< 50 – 2
< 69 – 3
< 84 – 4
≥ 85 – 5

5. Probability theory and mathematical statistics
in TSU
The goal of the course
The purpose of this course is to present basic information about the construction and analysis of models that take into
account random factors.
Output results
During this course, students should: master the basic concepts of probability theory and mathematical
statistics, master the basic techniques of formulating and solving probabilistic statistical problems.

6. SEFI. Level 0
CORE 0 TSU
interpret data presented in the form of line diagrams, bar charts, pie charts
interpret data presented in the form of stem and leaf diagrams, box plots,
histograms
construct line diagrams, bar charts, pie charts, setm and leaf diagrams, box
plots, histograms for suitable data sets
2/4 semester
calculate the mode, median and mean for a set of data items 2/4 semester
define the terms 'outcome','event' and 'probability' 2/ 4 semester
calculate the probability of an event by counting outcomes 2/ 4 semester
calculate the probability of the complement of an event 2/ 4 semester
calculate the probability of the union of two mutually-exclusive events 2/ 4 semester
calculate the probability of the union of two events 2/ 4 semester
calculate the probability of the intersection of two independent events 2/ 4 semester

7. SEFI. Level 1
LEVEL 1 TSU
calculate the range, inter-quartile range, variance and standard deviation for
a set of data items
2/ 4 semester
distinguish between a population and a sample 3/5 semester
know the difference between the characteristic values (moments) of a
population and of a sample
3/5 semester
construct a suitable frequency distribution from a data set 3/5 semester
calculate realtive frequencies 3/5 semester
calculate measures of average and dispersion for a grouped set of data 3/5 semester
understand the effect of grouping on these measures 3/5 semester
Combinatorics 2/4 semester
use the multiplication principle for combinations 2/4 semester
interpret probability as a degree of belief 2/4 semester
understand the distinction between a priori and a posteriori probabilities 2/4 semester
use a tree diagram to calculate probabilities 2/4 semester
know what conditional probability is and be able to use it (Bayes' theorem) 2/4 semester

8. SEFI. Level 1
calculate probabilities for series and parallel connections 2/4 semester
define a random variable and a discrete probability distribution 2/4 semester
state the criteria for a binomial model and define its parameters 2/4 semester
calculate probabilities for a binomial model 2/4 semester
state the criteria for a Poisson model and define its parameters 2/4 semester
calculate probabilities for a Poisson model 2/4 semester
state the expected value and variance for each of these models 2/4 semester
understand what a random variable is continuous 2/4 semester
explain the way in which probability calculations are carried out in the
continuous case
2/4 semester
Normal distribution 2/4 semester
relate the general normal distribution to the standardised normal distribution 2/4 semester
define a random sample 3/5 semester
know what a sampling distribution is 3/5 semester

9. SEFI. Level 1
understand the term 'mean squared error' of an estimate 3/5 semester
understand the term 'unbiasedness' of an estimate 3/5 semester
apply confidence intervals to sample estimates 3/5 semester
follow the main steps in a test of hypothesis 3/5 semester
understand the difference between a test of hypothesis and a significance test
(pvalue)
3/5 semester
define the level of a test (error of the first kind) 3/5 semester
define the power of a test (error of the second kind) 3/5 semester
state the link between the distribution of a normal variable and that of means
of samples
3/5 semester
place confidence intervals around the sample estimate of a population mean 3/5 semester
test claims about the population mean using results from sampling 3/5 semester
recognise whether an alternative hypothesis leads to a one-tail or a two-tail
test
3/5 semester
compare the approaches of using confidence intervals and hypothesis tests 3/5 semester

10. SEFI. Level 2
LEVEL 2 TSU
compare empirical and theoretical distributions 3/5 semester
apply the exponential distribution to simple problems 2/4 semester
apply the normal distribution to simple problems 2/4 semester
apply the gamma distribution to simple problems 4, 5 semester
understand the concept of a joint distribution 2/4 semester
understand the terms 'joint density function', 'marginal distribution
functions'
2/4 semester
define independence of two random variables 2/4 semester
solve problems involving linear combinations of random variables 2/4 semester
determine the covariance of two random variables 2/4 semester

11. SEFI. Level 2
determine the correlation of two random variables 2/4 semester
realise what the normal distribution is not reliable when used with
small samples
3/5 semester
use tables of the t-distribution 2/4 semester
use tables of the F-distribution 3/5 semester
use the method of pairing where appropriate 3/5 semester
use tables for chi-squared distributions 3/5 semester
decide on the number of degrees of freedom appropriate to a
particular problem
3/5 semester
use the chi-square distribution in tests of independence
(contigency tables)
3/5 semester
use the chi-square distribution in tests of goodness of fit. 3/5 semester
set up the information for a one-way analysis of variance 3/5 semester
Analysis of variance in another course
Simple linear regression, Multiple linear regression in another course

12. SEFI. Level 3
LEVEL 3 TSU
Stochastic processes 3 year (Stochastic processes)
Statistical quality control
Reliability 4 year
Experimental design
Queueing theory and discrete simulation 4 year (Simulation modeling), Master (Queueing theory)
Filtering and control 4 year
Markov processes and renewal theory 3 year (Stochastic processes), Master (Queueing theory)
Statistical inference
Multivariate analysis elective courses

13. in SEFI offline
ADD:
• Conditional distribution and conditional mean (3/5 semester)
• characteristic functions (3/5 semester)
• effective estimates (3/5 semester)
• information Fischer, inequality of Rao-Cramer (3/5 semester)
• central statistics, the construction of confidence intervals using central statistics (3/5 semester)
• methods of construction estimates (3/5 semester)
• likelihood function (3/5 semester)

14. Probability theory and mathematical statistics
in TSU
Modernization course:
• pre-test;
• homework in Math Bridge;
• tests on the topics in Math Bridge;
• bridging courses in Math Bridge.

15. Probability theory and mathematical statistics
in TSU: Modernization course
Pre-test (content):
• Theory of sets;
• combinatorics;
• graphs of functions;
• area of the figure;
• geometric progression;
• image of a set of points on the plane;
• diagrams.

16. Probability theory and mathematical statistics
in TSU: Modernization course
Pre-test (example):
1. Тридцать человек разбиты на три группы по 10 человек в каждой. Сколько может различных составов групп?
2. Сколько четырехзначных чисел, составленных из цифр 0,1,2,3,4,5 содержат цифру 3?
3.Садовник должен в течение 3-х дней посадить 10 деревьев. Сколькими способами он может распределить по дням работу, если
будет сажать не менее 1 дерева в день?
4. Расписание одного дня содержит 4 семинара. Определить количество таких расписаний из 9 дисциплин.
5. Какова вероятность того, что при двух подбрасываниях монеты герб появится один раз?
6. В группе 35 студентов. Каждый из них пользуется хотя бы одним из видов городского транспорта: метро, автобусом и
троллейбусом. Всеми тремя видами транспорта пользуются 6 студентов, метро и автобусом – 15 студентов, метро и троллейбусом –
13 студентов, троллейбусом и автобусом – 9 студентов. Сколько студентов используют только один вид транспорта?

17. Probability theory and mathematical statistics
in TSU: Modernization course
7. Первую или вторую контрольные работы по математике успешно написали 33 студента, первую или третью – 31 студент,
вторую или третью – 32 студента. Не менее двух контрольных работ выполнили 20 студентов. Сколько студентов успешно решили
только одну контрольную работу?
8. Найти суммы бесконечно убывающих прогрессий: a).
9. Построить график функции:
10. Изобразить с помощью линейной диаграммы тенденцию перевозок пассажиров общественным транспортом в России, если
имеются следующие данные:
Год
ы
2006 2007 2008 2009 2010 2011
Млн
.чел
.
4788
5
4811
4
4628
3
4503
7
4541
2
45817

18. Probability theory and mathematical statistics
in TSU: Modernization course
Homework in Math Bridge:
At the present time for homework developed methodological guidelines containing a brief theoretical material,
examples of problem solving and task list for homework.
It makes sense to use the platform Math Bridge for homework, use bank of available tasks.

19. Probability theory and mathematical statistics
in TSU: Modernization course
Bridging courses in Math Bridge (for example):
1. theory of sets;
2. combinatorics;
3. graphs of functions.
Since in our department to first-year students entered the leveling course of elementary mathematics, it is very convenient
in this course with the help of Math Bridge consider necessary topics.

20. Project MetaMath
Thank you for your attention!
zakhar_iv@mail.ru

21. Variants of the course project
1. Write a program that calculates the value of the function
• Random value has a t - distribution (Student distribution).
2. Write a program that calculates the value of the integral
• - function of distribution of betta – law, if - Euler gamma
function.
3. Write a program that calculates the area of the figure given lines