The first was Sonya Kovalevskaya

Noted for being the first Russian Female Mathematician. She was born January 15, 1850 in Moscow, Russia to General Krukovskaya. Sonya was had two other siblings.  Professor Kim told us that as a teen, Sonya wallpapered her room in mathematical lecture notes.  Years later, Sonya entered into a marriage of convenience with Vladimir Kovalevskaya. In 1868 the two moved to Heidelberg, Germany. In 1869 she was admitted to the University of Heidelberg. Sonya’s paper on Partial Differential Equations later gained her admittance to the university of Gottingen where she received an unofficial PHD. After leaving Germany, Sonya and Vladimir moved back to Russia where they gave birth to a daughter named Fufa.

After the child was born Sonya briefly retired from math.  However, in 1883, she was then offered a position a Stockholm University in Sweden, which she accepted. After about a year Sonya took over the editing position for the journal, Acta Mathematica. In 1888 she received the Prix Bordin for one of her works. In 1889 she was the first female granted tenor ship.  Shortly after, in 1891 She passed away at the age of 41.

Then we discussed Grace Chisholm Young

Born in London 1868, Grace led a charmed life. At age 17 she was admitted to Cambridge and by 21 she was attending the woman’s education program at Griton College. She soon met and fell in love with one of her professors, William Young. The two married latter married, forming a mathematical union, and moved to Gottingen to study under Professor Klein. At the age of  27 Grace became the first female mathematician to receive an official doctrine. Around 1906, the couple wrote a text about Set Theory and moved to Switzerland with their children. In 1940 Grace’s family left for Paris to escape the war while William remained in Switzerland. In 1942 he passed away, two years later so did Grace.

Lastly, we discussed Emmy Noether.

Born in 1882 Germany.  Emmy’s father, Max, was a mathematician University of Erlangen. Growing up, Emmy decided that she would teach. However, she later realized her passion was math, so she pursued it at the Erlangen. In 1907 she received her PHD from the university.  in 1919 she received the title of privatdozent, which met she was now recognized as a lecturer at the University of Gottingen, her students were referred to as the “Noether boys”. However, since she was a women, the university did not pay her. She was most noted for the “Noetherian ring” which dealt with her works in abstract algebra. Emmy left Germany during World War II and moved to the United States.

Emmy passed away at the age of 53 in Pennsylvania 1n 1935

Professor Kim began today’s class with a puzzle that related to the years of Mary Somerville’s birth and death.  It looked something like this: _ _ _ _ -_ _ _ _ .  We were then told that the first 2 digits of her birth year were also the 7th prime number, which we discovered was 17. The last two digits of her birth year are  equal the sum of the first two numbers, 10(7+1) = 80… 1780.For the year of death, Professor Kim explained that the last 2 digits were the reverse of the birth year, so 1 8 7. The last two digits of her year of death are the sum of the first two digits multiplied by the second digit, or, (1+8)X8=72. Which, in fact, was correct. Mary Somverille was born in  1780 and passed in 1872.

Then we discussed the Chladni Diagrams, which dealt with vibrations of sand patterns; a topic which interested Ms. Sophie Germain as well.

The idea was to spread the sand over glass plates and then run a violin bow over the edges to observe the patterns created through the vibration.

We also briefly discussed, ::Gasp:: Trigonometry AFTER Professor Kim gave us a colorful acronym to soften the blow. She wrote this sentence on the board “Some Old Hag Caught A Hippie Tripping On Acid.”

Sin(ø)= O/H or some old hag

Cos(ø)=A/H caught a hippie

Tan(ø)=O/H tripping on acid

This had something to do with a popularized scientific discovery; taking different consecutive terms until a constant difference (I think ??)

Our class ended with the introduction of the Fibonacci Rabbit  Sequence. Professor Kim told us that a single pair of rabbits one male and the other female are born at the beginning of a year… the rabbit are not fertile until the first month of life, but they do not give birth until the second month, I think(?) Anyway, the first two rabbit will give birth to a male/female pair at the end of each month and so on and so on. Given the conditions that no rabbits die. – How many pairs of rabbits will have been born by the end of one year?

Apparently there are different  number sequences involved as you can see in the video and also on the website, which gave the example of the sequence  1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 etc. I still don’t understand the problem, but the website above made a little more sence.

Mary Fairfax Greig Somerville – “born on December 26, 1780 in Jedburgh Scotland, the daughter of Margaret Charters and Lieutenant William George Fairfax, a vice admiral in the British Navy”. She had six other siblings.  Like many of the other women we’ve learned about, Mary was also self taught. By age ten Mary was sent to boarding school we’re she continued to pursue education.  At age 20 (1804) she married her cousin Samuel Greig, they had two sons before Sam passed in 1807. In 1812 she married William Somerville, yet another cousin. William was more willing to entertain the idea of an educated wife.  The couple had four additional children.

Mary was considered to be a great astronomer and mathematician.  In 1826 she presented a paper entitled The Magnetic Properties of the Violet Rays of the Solar Spectrum. Her second book The Connection of the Physical Sciences, was an account of physical phenomena among the physical sciences. Shortly after publishing her second book, she was admitted to the Royal Astronomical Society (1835).

Mary died in Italy at the age of 92!!

The second women we discussed was Ada Bron Lovelace, the only child born of famous poet Lord Byron.  Ada was actually Mary Somerville’s Protégé!  Around age 18 Ada began a correspondence with Charles Babbage, a math professor at Cambridge. The two are said to have created the first computer program. She passed away of cancer at age 37.

Ada also worked on The Tower of Hanoi problem: which consists of three rods, and a number of disks of different sizes which can slide onto any rod. The puzzle starts with the disks neatly stacked in order of size on one rod, the smallest at the top, thus making a conical shape.

The objective of the puzzle is to move the entire stack to another rod, obeying the following rules:

• Only one disk may be moved at a time.
• Each move consists of taking the upper disk from one of the pegs and sliding it onto another rod, on top of the other disks that may already be present on that rod.
• No disk may be placed on top of a smaller disk.

We also discussed “Humpty Dumpy Functions” which are easy to calculate, but difficult to reconstruct missing pieces. We were introduced to the formula x³ mod P=2

Notice the lack of patterns in the table.

Cryptography – is the practice and study of hiding information. We were given an example of Alice, Bob, and Eve. If Alice&Bob want to communicate without Eve knowing the discussion they would have to agree what to use, our example was 7^xmod 11. Alice chose 3 as her private number and Bob chose 6. Alice takes A and puts it into a function: a=7^A mod 11 which becomes a=7³=mod 343 mod 11=2. Bob takes his B and put it into a function b=7^B mod 11 and gets 7⁶=b=17649 mod 11=4. So then Alice takes Bob’s 4 and raises it to the power of 3 and then sends it back to Bob, who then takes that number and raises it to the power of 6.

*b⁴ = mod 11 = 4³ mod 11= 64 mod 11=9

*a^B = mod 11 = 2⁶ mod 11 = 64 mod 11 = 9

So a^B mod 11 = b^A mod 11  for any A&B

I think we may need to go over all of this again before I fully understand it… See You Next Tuesday Kiddos

We also discussed Ms. Sophie Germain’s Primes… A prime number is a Germain prime if 2p + 1 is also prime. For example, 23 is a Sophie Germain prime because it is a prime and 2 × 23 + 1 = 47, also prime. 7,11,23,47 are some examples of Germain primes.

Composite numbers are never prime!

We also learned about Perfect Numbers, which are numbers whose sum of its factors are equal to itself. 6 was our given example :6×1=6, 2+3+1=6, 2×3=6. However, perfect numbers are few and far between with 496 being next, followed by 8128. For the most part, it is believed that there are no odd perfect numbers, however since it has not been proven true it is simply a conjecture.

Speaking if conjectures led us to Goldbachs Conjecture – Every even number that is greater or equal to 4 can be written as a sum of two primes.

4= 2+2

6= 3+3

8= 5+3

10= 7+3 & 5+5

12= 7+5

14= 7+7 & 11+13

This discussion led us to a man by the name of Mersennea , a 17th century French scholar who created a list of numbers that were then named for him, Mersennea Primes.

Let P be a prime number: Mp=2^p-1

The prime numbers are 2, 3, 5, 7, 13

The corresponding Mersenne Numbers are 3, 7, 31, 127, 8191

11&2047 are not considered Mersenne because 2047 is not prime.

We finished class with a discussion of this therom- N is an even perfect number if and only if it has the form 2^p-1(2^p -1)

for example:

2 is prime 3 is Mersenne Prime 2^2-1 = 6

3 is prime 7 is Mersenne Prime 2^3-1= 28

5 is prime 31 is Mersenne Prime 2^5-1= 496

Her gender became more apparent but it wasn’t the problem she had originally assumed it would be.  In 1811 she submitted an experiment dealing with sand patterns to the French Academy of Sciences. She was the only applicant. It was returned to her twice, stating a flawed solution. However, this did not deter Ms. Germain, she re-submitted the problem and finally in 1816 she was awarded the prize.

She became interested in Fermat’s Theorem  and also experimented with soap film patterns and applied mathematics.

At the age of 55 Sophie passed away from breast cancer.

With limited sources of entertainment, Sophie  focused her time on education reading everything in her fathers library. Of course at this time it was unheard of for women to become educated. Her parents were distraught. They were convinced that her education would lead to her demise, so they tried on several occasions to cease her from learning, even going as far as to take away her clothing so that she was forced to stay in bed. But she would not be swayed. Finally her parents gave up discouraging her and decided to just let her be.

Within the next few years, as the revolution began to calm a bit, Sophie became interested in institutes of higher education. Unfortunately, being a women, acceptance into college was forbidden. But that didn’t stop her thirst for knowledge and she was given  lecture notes from her male friends. With those notes she taught herself and eventually wrote a paper which she submitted under a former male students name.

Once it was revealed to the professor that she had written the paper and not the male student, he began writing and mentoring Sophie. in 1801, at age 25, she began writing to Gauss, a German professor of mathematics, who was also very accepting to the fact that she was a women.

I believe that was all for today.

To Be Continued…..

By age nine Maria could speak several languages fluently. During parties her father would throw, she would “preform” for the guests by lecturing, in Latin, about  woman’s higher education.  By age thirteen she could speak five other languages (Greek, Hebrew, Spanish, Latin, French) in addition to her native Italian. She also wrote a book, Philosophical Propositions, which was a collaboration of over a hundred speeches recited at her fathers parties. She was well on her way to becoming a famous mathematician and philosopher.

in 1732, fourteen year old Maria lost her mother and therefore took over the household duties. While her father remarried, the other women contributed nothing more than twelve other children, whom Maria was left to care for. She took the education of her siblings seriously and created text books in which to teach them with.  At age twenty Maria decided to become a nun, but her father was against it so she never pursued it.

In 1748 she published a two volume book entitled Analytical Institutions “The first volume covered arithmetic, algebra, trigonometry, analytic geometry and calculus. The second volume covered infinite series and differential equations. No one before had published a text on calculus that included the methods of calculus of both Isaac Newton and Gottfried Liebnitz.” (About.com) By 1801 the book was translated into English by a professor from Cambridge.

At age thirty-four Maria’s father passed away leaving behind a devastated women with no where to turn. She began withdrawing from the math world because the work was reminiscent of her father and she no longer took pleasure in it.

In 1759 she established a home for poor women. In 1783 she was made Director of Home of the Ages where she lived amongst the poor women she cared for.   Her health had begun to deteriorate and she was now deaf and blind. By 1799 she had given away all of her possessions so when she passed away from heart failure she was buried in a paupers grave.

We were also introduced to Julia Robinson. As a child, she was not see as an extremely bright child. However, she wanted to learn how to solve mathmatical problems. In 1940 she attended San Diego State and then on to Berkley where she also got her Phd.  She was given an oppertunity to lecture at Berkley, though the position was not a permanant one it lasted some fifteen years. In 1974 Robinson became the first woman mathematician to be elected to the National Academy of Sciences, and was finally offered a permanant position as a professor. Unfortunately, In 1985 Julia passed away from cancer at age sixty-five.

I think that midterm was a diaster