Handbags -

The industrial revolution marked a turning point. As rail travel became popular, the need for sturdy, handheld luggage grew. This era saw the birth of the modern handbag as we know it, with brands like Louis Vuitton and Hermès transitioning from saddlery and trunk-making to creating smaller, portable bags for the mobile woman. Symbolism and Status

Historically, bags were purely practical. In the Middle Ages, both men and women wore pouches attached to their girdles or belts to hold coins and personal items. However, as clothing became more tailored and pockets were integrated into men’s trousers, women’s fashion moved toward voluminous skirts that necessitated separate, detachable bags known as "reticules." HANDBAGS

In the 20th and 21st centuries, the handbag transformed into a definitive status symbol. The emergence of "designer" culture turned specific silhouettes into icons. For example, the Hermès Birkin and the Chanel 2.55 are not just accessories; they are investment assets that often appreciate in value more reliably than the stock market. The industrial revolution marked a turning point

Today, the handbag industry is facing a shift toward ethical consumption. While the allure of luxury remains, there is a growing demand for vegan leathers, recycled textiles, and "slow fashion" pieces. Designers are increasingly pressured to balance the aesthetic appeal of a bag with its environmental footprint. Furthermore, the rise of gender-neutral fashion has brought the "murse" (men's purse) and unisex slings into the mainstream, proving that the handbag’s utility transcends gender boundaries. Conclusion Modern Trends and Sustainability

The handbag is a unique object that sits at the intersection of private necessity and public display. It tracks the progress of technology, the shift in social hierarchies, and the evolution of personal taste. Whether it is a vintage heirloom or a modern sustainable tote, the handbag remains an essential extension of the self, carrying our world within its seams.

Beyond wealth, handbags reflect the lifestyle and autonomy of the wearer. A professional might opt for a structured tote that fits a laptop, signifying career ambition, while a minimalist might choose a small crossbody bag, reflecting a "less is more" philosophy. The handbag is a portable "room of one’s own," containing a curated collection of a person’s private life—keys, phone, makeup, and memories. Modern Trends and Sustainability

Written Exam Format

Brief Description

Detailed Description

Devices and software

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The industrial revolution marked a turning point. As rail travel became popular, the need for sturdy, handheld luggage grew. This era saw the birth of the modern handbag as we know it, with brands like Louis Vuitton and Hermès transitioning from saddlery and trunk-making to creating smaller, portable bags for the mobile woman. Symbolism and Status

Historically, bags were purely practical. In the Middle Ages, both men and women wore pouches attached to their girdles or belts to hold coins and personal items. However, as clothing became more tailored and pockets were integrated into men’s trousers, women’s fashion moved toward voluminous skirts that necessitated separate, detachable bags known as "reticules."

In the 20th and 21st centuries, the handbag transformed into a definitive status symbol. The emergence of "designer" culture turned specific silhouettes into icons. For example, the Hermès Birkin and the Chanel 2.55 are not just accessories; they are investment assets that often appreciate in value more reliably than the stock market.

Today, the handbag industry is facing a shift toward ethical consumption. While the allure of luxury remains, there is a growing demand for vegan leathers, recycled textiles, and "slow fashion" pieces. Designers are increasingly pressured to balance the aesthetic appeal of a bag with its environmental footprint. Furthermore, the rise of gender-neutral fashion has brought the "murse" (men's purse) and unisex slings into the mainstream, proving that the handbag’s utility transcends gender boundaries. Conclusion

The handbag is a unique object that sits at the intersection of private necessity and public display. It tracks the progress of technology, the shift in social hierarchies, and the evolution of personal taste. Whether it is a vintage heirloom or a modern sustainable tote, the handbag remains an essential extension of the self, carrying our world within its seams.

Beyond wealth, handbags reflect the lifestyle and autonomy of the wearer. A professional might opt for a structured tote that fits a laptop, signifying career ambition, while a minimalist might choose a small crossbody bag, reflecting a "less is more" philosophy. The handbag is a portable "room of one’s own," containing a curated collection of a person’s private life—keys, phone, makeup, and memories. Modern Trends and Sustainability

Math Written Exam for the 4-year program

Question 1. A globe is divided by 17 parallels and 24 meridians. How many regions is the surface of the globe divided into?

A meridian is an arc connecting the North Pole to the South Pole. A parallel is a circle parallel to the equator (the equator itself is also considered a parallel).

Question 2. Prove that in the product $(1 - x + x^2 - x^3 + \dots - x^{99} + x^{100})(1 + x + x^2 + \dots + x^{100})$, all terms with odd powers of $x$ cancel out after expanding and combining like terms.

Question 3. The angle bisector of the base angle of an isosceles triangle forms a $75^\circ$ angle with the opposite side. Determine the angles of the triangle.

Question 4. Factorise:
a) $x^2y - x^2 - xy + x^3$;
b) $28x^3 - 3x^2 + 3x - 1$;
c) $24a^6 + 10a^3b + b^2$.

Question 5. Around the edge of a circular rotating table, 30 teacups were placed at equal intervals. The March Hare and Dormouse sat at the table and started drinking tea from two cups (not necessarily adjacent). Once they finished their tea, the Hare rotated the table so that a full teacup was again placed in front of each of them. It is known that for the initial position of the Hare and the Dormouse, a rotating sequence exists such that finally all tea was consumed. Prove that for this initial position of the Hare and the Dormouse, the Hare can rotate the table so that his new cup is every other one from the previous one, they would still manage to drink all the tea (i.e., both cups would always be full).

Question 6. On the median $BM$ of triangle $\Delta ABC$, a point $E$ is chosen such that $\angle CEM = \angle ABM$. Prove that segment $EC$ is equal to one of the sides of the triangle.

Question 7. There are $N$ people standing in a row, each of whom is either a liar or a knight. Knights always tell the truth, and liars always lie. The first person said: "All of us are liars." The second person said: "At least half of us are liars." The third person said: "At least one-third of us are liars," and so on. The last person said: "At least $\dfrac{1}{N}$ of us are liars."
For which values of $N$ is such a situation possible?

Question 8. Alice and Bob are playing a game on a 7 × 7 board. They take turns placing numbers from 1 to 7 into the cells of the board so that no number repeats in any row or column. Alice goes first. The player who cannot make a move loses.

Who can guarantee a win regardless of how their opponent plays?

Math Written Exam for the 3-year program

Question 1. Alice has a mobile phone, the battery of which lasts for 6 hours in talk mode or 210 hours in standby mode. When Alice got on the train, the phone was fully charged, and the phone's battery died when she got off the train. How long did Alice travel on the train, given that she was talking on the phone for exactly half of the trip?

Question 2. Factorise:
a) $x^2y - x^2 - xy + x^3$;
b) $28x^3 - 3x^2 + 3x - 1$;
c) $24a^6 + 10a^3b + b^2$.

Question 3. On the coordinate plane $xOy$, plot all the points whose coordinates satisfy the equation $y - |y| = x - |x|$.

Question 4. Each term in the sequence, starting from the second, is obtained by adding the sum of the digits of the previous number to the previous number itself. The first term of the sequence is 1. Will the number 123456 appear in the sequence?

Question 5. In triangle $ABC$, the median $BM$ is drawn. The incircle of triangle $AMB$ touches side $AB$ at point $N$, while the incircle of triangle $BMC$ touches side $BC$ at point $K$. A point $P$ is chosen such that quadrilateral $MNPK$ forms a parallelogram. Prove that $P$ lies on the angle bisector of $\angle ABC$.

Question 6. Find the total number of six-digit natural numbers which include both the sequence "123" and the sequence "31" (which may overlap) in their decimal representation.

Question 7. There are $N$ people standing in a row, each of whom is either a liar or a knight. Knights always tell the truth, and liars always lie. The first person said: "All of us are liars." The second person said: "At least half of us are liars." The third person said: "At least one-third of us are liars," and so on. The last person said: "At least $\dfrac{1}{N}$ of us are liars."
For which values of $N$ is such a situation possible?

Question 8. Alice and Bob are playing a game on a 7 × 7 board. They take turns placing numbers from 1 to 7 into the cells of the board so that no number repeats in any row or column. Alice goes first. The player who cannot make a move loses.

Who can guarantee a win regardless of how their opponent plays?