Friday, December 11, 2015

MTH 495 Recap

Growing up in grade school I was never a fan of history. Yeah, I think some of the events in history were interesting to learn and hear about, but as a whole it did not grab my attention. A typical history class in grade school I thought of was just grading you on how well you knew the sequence of events and the dates in which they happened, who was in involved, and the what the outcome was. It was a memorization type course. There is a reason why I am a Math major. That is because my mind and brain thinks in a systematic process. 
I would have to admit, I was a bit apprehensive about taking this course. Not because this was my senior capstone course to graduate, but by the title of the course: Nature in Mathematics. This title means history. A word that I am not a huge fan of. 
After the first couple of weeks of class, I realized that although we are talking about the history of math, I really enjoyed learning about who and how math was discovered or invented (depending on what you believe). 

One topic that we discussed that I will never forget is infinity. We as a class discussed and debated if infinity was a number. If I was a elementary student first seeing the infinity symbol:

I would say that yes, it is a side-ways eight. Although, we all know that infinity is not a side ways is bigger than the biggest number we know of. Similarly, negative infinity is smaller than the smallest number we know. I believe that infinity is not a number, it is just a symbol representing a limit beyond what we would expect. I believe this because we cannot do operations on infinity and obtain another number. For example, What is infinity*infinity? maybe it is infinity squared, but then what is that? 
Another topic within infinity that still blows my mind is the Aristotle's Wheel. 

Just like this one day in class talking about infinity, there were multiple other days that I really enjoyed attending. All the topics covered helped me completely understand the topic at hand. Although, I have learned about most the topics before hand in other courses, I only knew the concept, process, why, when, and where you apply it. I did not know where it came from, who originally proved that the topics are true. 
Learning the back story behind the topics was eye opening. Some of the mathematicians that we discussed this semester spent most of their lives learning, teaching themselves, and researching math. Mathematicians are truly dedicated to their work. I still think it is crazy that it took Andrew Wiles seven years to complete Fermat's Last Theorem and when written completely out it is over 150 pages long. 

Looking at on this semester in class, I really have enjoyed it and feel like I know the concepts and topics more even though we hardly did any math or problems throughout the course. Simply learning about how the concepts became was the icing on the cake for me. 

And yes I may like history a little bit more now. :) 

Monday, December 7, 2015

The History of Women in Mathematics

As a female in a Science, Technology, Engineering, and Mathematics (STEM) field I am very interested and aware of the way women are viewed in these fields. Upon graduation in April I hope to inspire other females to pursue whatever field of study they want and don't be afraid of stepping outside the gender norms. Being a resident and peer mentor of the Women in Science and Engineering (WISE) resident hall, has helped me achieve my goals. I have had multiple discussions with other women on our studies and how at times it can be hard, but in the end we achieve what we set out to do.  I think a majority of this is from the support of other females in STEM fields and peers. I know for myself and I am sure of other females, we like to reach out and ask for help when we don't understand; males not so much.
During my math capstone course we took a day to look at Sophia Germain. This was the first time I learnt about female in the math field. Before, I knew that mathematics had some female mathematicians in their history, but I never knew who and what they contributed. This class got me interested in learning about other female mathematicians. Below are some that I found a read up on their life, what they contributed, and when.

Hypatia ~370 AD - 415 AD
Born in Alexandria, Egypt to a father whom was also a mathematician, she had a great supported. Theon, her father, had a different philosophy to raising his daughter than most others at the time. He wanted her to know and think that she could do anything that she put her mind to. Thus, expressed education and physical activity were good to have to help you succeed. Following in her fathers footsteps, Hypatia, eventually surpassed his knowledge and at this point he sent her to Athens to study mathematics. After completely her studies, she returned to Egypt and taught. While teaching, she continued to do research. In her research, she is most known for coming up with the idea of hyperbolas, parabolas, and ellipses. Because of her teaching abilities she was able to explain the tough, dense math topics and ideas to other easily. Although she contributed a lot to the math community her life ended tragically in a murder, because others thought she was a witch and doing black magic, when she was just developing math concepts!

Image result for Emmy NoetherEmmy Noether 1882 - 1935
Noether was born in Germany to her parents. From a young age, she was always interested in math. However, she received her teaching certification for foreign languages. Even after this period in her life, she had that passion and love for math she wanted to pursue. Although she was not able to registrar for her classes because of her gender, she was allowed to sit in on the course; so she did. Finally she was able to enroll in classes and after about three years of studies she received her math degree. After graduating, she continued to study and research mathematics. She is best known for her research in abstract algebra. The Noetherian rings are named after her. She also helped develop the axiomatic approach to math. 

Image result for Sofia Kovalevskaya
Sofia Kovalevskaya 1850 - 1891 
Kovalevskaya's bedroom wall paper were her fathers calculus notes. This is where she started to learn math and teach it to herself. Although, this is not what her parents wanted her to do. They forbidden her from teaching herself mathematics and studying the subject, because they believed that women should not have a higher education. That's where Kovalevskaya hid in her room and studied mathematics. She taught herself trigonometry in her teen years and after completing her secondary education continued on to an university. She complete her degree and went on to do research.

Image result for sophie germainSophie Germain 1776 - 1831 
Germain is a French, self-taught mathematician. All of her material for which she taught herself was from her male friends whom were able to attend the school. Her parents were opposed of her studying mathematics so they took her light and candles away at night. But at night she would use the candles she smuggled and continued her studies. She is best known for a limited proof Fermat's last theorem, for prime numbers under 100. She has won prizes for her work. Germain was praised by male mathematicians of her work. Gauss especially liked her number theory proofs. She died at the age of 55 due to breast cancer.  

It was interesting to look and learn about some women mathematicians and the struggles that they had to go through to pursue their passion. From females not even allowed to enroll in a university, to parents saying no, they all overcame the obstacles and pursued their dreams. I couldn't imagine going through what all three of the above women did. But it also made me realize that if you truly believe in what you love, you can achieve it. Learning about these three women have added to my experience as a female math student to work hard and never give up no matter what others think or feel.

and MTH 495 notes