## And then there were three…

**Sonya Kovalevskaya**

Sonya Kovalevskaya(Sofia) was born in Moscow, Russia in 1850. She was not only a mathematician but a writer as well. Her father was General Krukovskaya and her mother Elizabeth. Sonya was the middle child of three siblings in her family. When she was 15 years old, she received her first lesson in calculus. Her bedroom walls were said to have lecture notes of integral and differential calculus on them. She also read a physics book that her neighbor had written. Later on, she met a man named Vladmir Kovalevskaya whom she married.

In Russia, women were not allowed to be educated at Universities let alone be mathematicians. In September 1868, she and Vladimir went to Heidelberg, Germany. Her intention was to attend the University of Berlin but they did not allow women either. However, she met Professor Weirstrass ( the father of analysis) at Berlin and he took her under his wing. With his guidance, she wrote 3 papers, 2 of which were in the mathematics field. “Partial Differential Equations” was submitted to Gottingen University and was found to be great work. She received her PH.D. from Gottingen because of this.

Sonya and her husband went back to Russia years later. They had a daughter named Fufi. There were no jobs in Russia and they had to live off of Sonya’s inheritance money from her father. Eventually, they left Russia again to live in Sweden where Sonya had the support of Mittag-Leffler.

Sonya obtained a teaching job at the University of Stockholm in 1883. She also became editor of the new journal, “Acta Mathematica”. This Univeristy awarded her tenorshop in 1889, the first to ever do so to a woman. Sonya also received the Prix Berdin award on Christmas Eve in 1888 for her work on differential equations.

Unfortunately this intelligent woman died in 1891 at the age of 41 of pneumonia.

**Grace Chisholm Young**

Her life was the most stable compared to the other two women discussed. She was born in London, England in 1868 to a retired warden and his wife. She was the youngest of three siblings.

At age 17, Grace passed the Cambridge exam and attended Gritoncollege (women education at Cambridge)when she was 21 years old. She initially to study medicine but it was not allowed for women at that time. Grace later attended Gottingen University and received her official PH.D. in mathematics. She was the first woman to ever have an official doctrine.

Not only did Grace get an education at Cambridge but there is where she found a husband. William Young was her instructor at the University and she later married him. The couple not only raised 6 children together but worked together as a mathematics union. They moved to Switzerland for occupational purposes. In 1906 they wrote on set theory together. Their children also became successful mathematicians, doctors, and scientists.

In 1940, Grace and some of her children returned to England. Her husband stayed in Switzerland where he died in 1942. Grace died in 1944.

The interesting thing about this lecture was Professor Kim mentioned that she knows Grace’s grand-daughter, Sylvia Wiegand who is a professor at the University of Nebraska. I thought that was kind of neat.

**Emmy Noether**

Emmy was born in Germany in 1882. Her father was a famous mathematician at the University of Erlangen. Her initial goal in life was to become a foreign language teacher but she had a passion for math and attended the University of Erlangen to pursue it. In 1907, she received her PH.D. of philosophy at Erlangen even though she had a passion for math…interesting.

In 1915, Emmy became a *privatdozent*( lecturer) at the University of Gottingen with the help of Professor David Hibert. but did not receive pay. She was a mentor to many students known as “Noether’s boy’s”.

She is famous for the Noetherian Ring in dealing with abstract algebra and contributions to theoretical physics.

Since Emmy and her family were of Jewish decent, when Hitler came to power she left Germany and moved to the United States. Emmy got a job at Bryn Mour, a women’s college in Philadelphia. However, Emmy died in 1935 after surgery.

## Under the guidance of Professor Kim

Well the class that we had to today that I’m about to blog about was a sad one. If you weren’t in class we heard that our professor’s father passed away. My thoughts and prayers go out to you and your family during this difficult time.

First of all, I give credit to Krista for explaining this much better than I could. Anyways, here’s my summarized version of what we covered.

Professor Kim started off the class with a puzzle. At first I thought it was the game hangman but i was mistaken. So she wrote _ _ _ _ _ _ _ _.

10 (1+7)=80

(1+8)x8=72

The last two digits of death year equals the number which is the product of the sum of the first two digits by the 2nd digit.

Now that I was offically confused for the remainder of the class, we started talking about Chladni Diagrams “Connection of the physical sciences” (1854) section of vibrations of surfaces.

- By spreading fine powder over glass plates, and running a violin bow over their edges.
- Reflection along the line one type of plane symmetry.

“To Chladni is due to the whole discovery of the symmetrical forms of modal lines in vibrating plates.”

deflection is the mirror image along the line through the center of a square.

-from Krista’s page

http://mathworld.wolfram.com/Cycloid.html

Pendulum -> Cycloid-curve traced out by a point P on the circumference of a circle as the circle rolls along a straight line.

1. Pendulum work which leads to cycloid

2. Symmatry of a square

Fibonacci sequence-a single pair of rabbits (male/female) is born at the beginning of a year.

Assume the following conditions:

1.) Rabbit pairs are not fertile during their first month of life but after give birth to one new pair (male/female) at the end of every month.

2.) No rabbits die

Now that I’ve confused everyone who just read this, I recommend you check out Krista’s blog because it’s pretty great! So check it out! http://kvieira.wordpress.com/

The next thing we did was pretty funny. Professor Kim was trying to explain Trig to us. She explained it like this which was hilarious!

**S**ome **O**ld **H**ag **C**aught **A** **H**ippi **T**ripping **O**n **A**cid

We heard about Sin, Cos, and Tan.

## Mary Fairfaux Greig Somerville 1780

In class we learned about Mary Fairfaux Greig Somerville.

Somerville was the daughter of William Fairfaux. Her father was on a sea voyage when she was born. Mary was 1 of 3 children. Her father didn’t encourage her when it came to her education, but her mother taught her how to read, not write.

By the time she was 10 years old, she was sent to a boarding school, but mostly educated herself. Her uncle also encouraged her to be educated. She also learned to speak Latin.

In 1804 she married Greig but he died 3 years later after she bore 2 children from him. He did not support her work with mathematics. Later on, she married her cousin William Somerville in 1812 who did support her mathematics career.

“Her work was very important to her and she had many accomplishments. She was considered a mathematician and an astronomer. She took part in the discussion of hypothetical planet perturbing Uranus and lead Adams to his investigation of this idea. She published *Magnetic Properties of Violet of Solar Spectrum* in 1826. In 1827 she rewrote *Laplace.* She also became a woman member of the Royal Astronomical Society in 1835.” -Borrowed from Krista Viera

In 1848 she wrote one of her first books, *Mechanisms of the Heavens, *a popularized account of Laplace’s “Celestial Mechanics”. And even at age 89, she continued to write and produced *Molecular and Microscopic Science. *Mary died at the age of 92 in Naples, Italy.

Ada Byron, Countess of Loveless.

Ada is the only biological child of Lord Byron, who was a famous romantic poet. She was born in 1815 in London, England. She was a woman of the genius type so to speak. She was also educated at home as was Mary.

There is another connection between Ada and Mary. Ada’s mother, Lady Byron, was good friends with Mary Somerville. Mary took Ada under her wing and helped her with math.

When Ada was 18 years old, she met Charles Babbage, a professor of mathematics at Cambridge. He is known as the father of modern computers (difference engine, analytical engine). The two began a correspondence of mathematical topics.

Because of her correspondence with Babbage, Ada is credited with the idea of computer algorithm (difference algorithm). She is considered an analyst and meta-physician

The Tower of Hanoi problem from french mathematician Lucas. The problem is: *What is the minimum number of ways moving disks one by one from pole A to pole C under the condition that no larger disks sit above smaller disks?*Professor Kim introduced this problem in class today. We went up to trying to move 4 disks. We found out it would take 15 movements to accomplish this problem with 4 disks. The function is : f(4)=2xf(3)+1 it is recursive.

## Prime number continuation…

Goldbach’s conjective

-any even number greater than or equal to 4 can be written as a sum of 2 prime numbers.

Ex: 16=13+3 = 11+5

Mersenne numbers

-any number that can be

M=2n-1

We also learned how many prime numbers there are in an infinite amount.

Euclie 25 centuries ago B.C. 4th century. He showed that is MP is a Mersenne prime.

In 1700’s Eucler showed that all even perfect numbers have this form.

Conjecture: only a finite number of Fn are prime.

Conjecture: only Fo, F1, F2, F3, F4 are prime.

Take an odd prime P form 2p+1 if Sp n 2P+1 is prime, then it’s called a Germaine prime. A number that is not prime is a composite number.

## Prime numbers

So we actually began working with numbers in the math class and I was reminded why I don’t like math all over again haha. Here we go…

A definition of a prime: a number that can only be divided by itself and one.

Number theory: The study of whole new integers. A perfect number is a number whose sum of divisions is equal to itself.

EX: 6=2 x 3 6=2+3+1

1 x 6

Other perfect numbers

“28”

2 x 14

4 x 7

1 x 28

2+14 + 4+7 +1=28

Conjecture: There are no odd perfect numbers

even number bigger or equal to 4

4= 2+2 16=13+3=11+5

6= 3+3 18=11+7

8=5+3 20=7+13

10= 7+3, 5+5 22=19+3=11+11

12=7+5 24=19+5=11+13

14= 7+7= 11+3

Goldbach’s conjecture: Every even number (n=4) can be written as a sum of 2 primes.

Sophie Germain has a prime number named after her.

We also did this graphing thing which I was lost completely. It looked like this..

Mp= 2p-1 ->look at the number Measure numbers

p Mp prime? P Mp 2ndMp

2 3 YES 2 3 6

3 7 YES 3 7 28

5 31 YES 5 31 496

7 127 YES 7 127 8128

11 2047 NO

13 8191 YES

First Mersenne prime was in 1456

Mersenne was the first one who put list of prime numbers

The number is not always prime if it is mersenne prime

Thm: n is a even perfect number if and only if it has the form 2 p-1 (2p – 1) –> 2 p-1 MP

## Julia Robinson

Julia Robinson was born 200 years after Marie. Julia was born in 1919. She was not brilliant and she spoke very late. She scored low average range in junior high. She was extremly shy. Her family evenatually moved to San Diego. There, she went to a univeristy there. She worked towards her Ph.D. in Berkley. She became married and she held a lecture position for 15 yrs. No one hired her to take a higher position because her husband worked there. The National Academy of Science elected her and after that happened she got hired as a professor. She was elected president at the mathematical society.

She died at 65 in 1976 before she got her professorship.

In 1983, she was awarded the McGarther Genius Award.

## Marie Agnesi

Marie Agnesi 1718-1749

She lived until about the age of 79 and was the oldest daughter out of 21 siblings to her parents. She was born in Italy. Her paternal grandparents were wealthy merchants. In Marie Agnesi’s family, her father was

If you weren’t wealthy, you couldn’t read or write. In Italy, women didn’t read. Men did. Unlike French women who did read.

If you were a woman in Italy, you were sent to a convent to pray, embroider things, etc.

In Marie Agnesi’s family, her father was not employed in comerse. He loved to have large parties. Her father encouraged her talents.

When she was 9, she knew several languages and translated speeches into Latin.

By the time she was 13, she spoke Hebrew, Greek, Spanish, English and Latin. During that time, you had to be able to speak Latin. She also was reading Newton’s ideas.

Her father wanted he rto learn more and she strived on it. She was a mathematician, philosopher and bottom line genuis.

While 14, her mother died while giving birth to the 8th child.

Throughout her teens, 20’s, 30’s, she took care of her siblings.

She took education seriously towards her siblings. Scholars considered work to be exceptional by the time she was 17. She once wanted to become a nun.

In 1742, her father passed away. This was very devastating to her. She lost everything that was pushing her. She continued to work in the field and it was hard for her.

When her father became ill, she took over his lectures.

In 1759, she moved to a rental house where she helped poor people.

She taught religious class to working people. She was Roman Catholic and sold jewelry that was given by the pope.

By the time she was 40 she left the math field. She moved into a home for women in mathematics.

As she got older, she got more ill.

In 1799, she had fluid in her chest and she died at 81 of heart failure. Back then, 81 was ancient.