Moscow Mathematical...

58

Moscow Mathematical…

Mathematics is needed in everything. It is needed in natural scientific research, engineering calculations, and various types of economic management systems.

Necessary mathematicians, the ability to solve problems related to the use of mathematical methods and computer technology in various fields of science and human activity. Such mathematicians are called specialists in applied mathematics.

Being a specialist in applied mathematics is difficult, but interesting and exciting. He must know, firstly, what to apply (general mathematics science), secondly, how to apply (special mathematical sciences), and thirdly, what to apply (specific issues of science and human activity).

Such specialists are trained at the Moscow Mathematical Technical Institute of the Ministry of Industry, Automation and Control Systems of the USSR *).

Moscow Mathematical Technical (MMT) has existed since 1967 and has already given two graduations on the basis of a 10-year school and one graduation on the basis of an 8-year school.

The duration of study at MMT for those who have completed the 8th grade of secondary school is 2 years 10 months, and for those who have completed the 10th grade - 1 year 10 months. Graduates receive the qualification “computer-mathematician” in the specialty “Applied Mathematics”.

They are prepared to work in computing and research centers, departments and laboratories, in design and engineering bureaus, and in enterprises.

In his work, a computer mathematician develops algorithms for solving problems on electronic computers, creates and uses programs for solving problems, implements solutions on the machine and analyzes the results obtained. Therefore, he must have a high mathematical culture. For this purpose, it is indicated that general mathematical disciplines are studied in MMT (algebra, geometry, mathematical analysis, linear algebra and analytical geometry, mathematical logic, probability theory), and special mathematical disciplines (linear and nonlinear programming, computational mathematics, programming and algorithmic languages, operations research, application of mathematical methods in natural scientific research, in automation and control systems, in solving economic problems). Those admitted after 8th grade also receive general secondary education.

In order to enroll in MMT after completing grades 8 or 10, it is enough to pass an oral exam in mathematics and a written exam in literature.

Each math exam ticket includes both theoretical questions and several exercises. When answering questions, the applicant is required to present the question clearly and mathematically correctly. When solving problems, you must be able to carefully justify each step of the solution, providing all the necessary references to the relevant definitions, aximons and theorems.

59

The exam also asks additional questions about theory and its application in solving problems; the content of tickets and additional questions does not go beyond the scope of the school curriculum.

Here are samples of exam paper options from 1970

Option for those who have completed 8th grade

1. Extracting the square root of a product.
2. Sine, cosine and tangent angle and their meanings for an angle of 60°.
   3 a) Perform actions:

$$\left(13 \frac{1}{4} - 2 \frac{5}{27} - 10 \frac{5}{6}\right) \cdot 230.04 + 46.75$$

0,01

6. Solve the system of equations:

$$\begin{cases} x^2 = 20 - y^2, \\ x + y = 6 \end{cases}$$

c) In an equilateral trapezoid, the bases are $k$ cm and $l$ cm. The diagonals are mutually perpendicular. Find the area of ​​the trapezoid.

Option for those who have completed 10th grade

1. Exponential function, its properties and graph.
2. Signs of parallelism of straight lines and planes.
   3 a) Simplify:

$$\left[ \frac{\frac{1}{2} + y}{\frac{1}{2}} - \frac{(x + y)}{\frac{1}{2}} \right]^{-2} - \frac{x + y}{2Vxy}$$

6. Solve inequality:

$$\log_2 x - 3 x > 1$$

c) Find the value of $M(x)$ if $M(x) = \text{tg} 6x + \sec 6x$, $\text{tg} 3x = 2$ and $0 < x < \frac{\pi}{6}$.

All that remains is to tell you the address of MMT: Moscow, E-43, Nizhnyaya Pervomaiskaya, 14 (there is no public service with equipment yet).

A. G. Terushkin

To note «Kvant»
for younger students

(see «Kvant» No. 4, 1971, 3rd cover page)

1. Note that for each break we notify the number of pieces per one. The total number of pieces is $4 \times 8 = 32$. Before breaking we had one piece, after the first breaking there were two, after the second breaking there were three, …, after the 31st breaking there were 32. Thus, in each order we break the chocolate bar, we will always have to break it exactly 31 times.

2. The cipher is as follows: hard vowels are replaced with their corresponding soft vowels, and soft vowels with hard ones ($a$ with $r$, $y$ with $l$ and $t$. D.); similarly, voiced consonants are replaced by glyhnye, and glyhnye by their corresponding voiced ones ($b$ to $n$, $b$ to $\phi$, $2$ to $k$ and $t$. D.); In addition, the hissing and whistling consonants ($\mu_1 - \mu$, $x - \mu$) and signs $7 - b$ have been rearranged.

Answer:
Our Tanya is crying loudly,
I dropped a ball into the stove.
Hush, Tanechka, don’t cry,
The ball will not sink in the stove.

3. The required method is shown at figure 1.
4. 7 375 428 413:125 473=58 781.
5. The new arrangement of matches is shown at figure 2.