Know Thy Self

My grandparents on my dad’s side were from family farms, and it was expected that they would go to school and work on the family farm. School was mainly to learn to read, write, and do basic math. So 8th grade was considered enough education and so they joined the family farms to work full time after that point.
  My grandparents on my mother’s side were from the city. They needed to get jobs in the city and the best way to do that was to graduate high school. Although, they lived during the same time period and their education was higher working was the main goal.
  My parents were both children of the baby boom. Math and Science were stressed in school, especially high school. Both of my parents came from big families (mom 11 dad 9) and they were older children. Even though one came from a farm and one the city, their parents felt they were doing the best for them and kicked them out of the house at age 18. College was a decision time for my parents to decide what they wanted to do in life. Mom went to college to get a degree and start working or get married whichever came first. Dad knew he was good with his hands and got degrees in electronics and automotive repair before getting a job as a mechanic. Dad currently (and for the past 20 years) works for the City of Fargo where his mechanic knowledge comes in handy. He uses the other half of his college education now working on hobby projects. My dad loves fixing T.V.s and computers in his spare time.
  When I was growing up my parents stressed that school was extremely important (a big difference from my grandparents). I worked hard and did well through high school. College was different, I worked hard however anxiety was a big factor for me and I was self-defeating. I left school for a while and eventually figured out my anxiety issues (although some days are still bad). I am now back in college being educated for me. I could work in nearly any job requiring a high school diploma and had a promising job, but I want to teach. I am still undecided as to whether I want to pursue my masters. However, I want to give children the best chance at learning so, although it may not be formal education, I never plan on quitting my education.

Mathematicians Report

Amalie Emma Noether: (1882-1935) Germany

Amalie Noether was a pioneering mathematical researcher. She was born in Erlangen, Germany on March 23, 1882. She was named Amalie, but always called "Emmy". She was the eldest of four children, and Mathematics seemed in her bloodline. Her father was Max Noether, a noted mathematician of his time, and her brother Fritz also made a career of mathematics.

      At the age of 18, Noether chose to take classes in mathematics at the University of Erlangen. Her brother, Fritz, was a student there, and her father was a professor of mathematics. Due to the fact she was a woman, the university refused to let Noether take classes. They did grant her permission to audit classes, however. She sat in on classes for two years, and then took and passed the exam that would permit her to be a doctoral student in Mathematics. This put her in good standing with the school. After five more years of study, she was granted the second ever degree to a woman in the field of Mathematics. The first had graduated a year earlier.

Emmy Noether made several major advances in abstract algebra. She originated novel reasoning methods, especially one based on "chain conditions.” Also, her perseverance about generalization led to a unified theory of modules and Noetherian rings. Her methods tended to unify disparate areas (algebra, geometry, topology, logic) and led eventually to modern category theory. Also, her origination of homology groups revolutionized topology.

Emmy Noether's work has found various applications in physics, and she made direct advances in mathematical Physics as well. Noether's Theorem established that certain symmetries imply conservation laws. This theorem has been noted as the most important theorem in physics since the Pythagorean Theorem.

Emmy Noether was not just great in Mathematics, she was a great person. She was generous with students and colleagues, even allowing them to claim her work as their own. Noether was close friends with other greatest mathematicians of her generation.  Hilbert, von Neumann, and Weyl were among her friends. Weyl once said he was embarrassed to accept the famous Professorship at Göttingen because Noether was his "superior as a mathematician." Few would dispute that Emmy Noether was the greatest female mathematician ever.

Archimedes of Syracuse (287-212 BC) Greek domain

Archimedes is commonly recognized to be the greatest of ancient mathematicians. He studied at Euclid's school (likely after Euclid's death), but his work far bested the works of Euclid. His achievements are particularly impressive given the lack of proper mathematical notation during his life. His proofs are noted not only for brilliance but for unsurpassed simplicity.

Archimedes made advances in number theory, Algebra, and analysis, but is most renowned for his many theorems of plane and solid Geometry. He was first to prove Heron's formula for the area of a triangle. One of his most remarkable and famous geometric results was determining the area of a parabolic section, for which he offered two independent proofs, one using his Principle of the Lever, the other using a geometric series. Many of Archimedes' discoveries are known only in the second-hand: Pappus reports that he discovered the Archimedean solids. Thabit ibn Qurra used Archimedes’ method to construct a regular heptagon. Also, Alberuni credits the Broken-Chord Theorem to him.

Archimedes anticipated integral calculus, most notably by determining the centers of mass of hemisphere and cylindrical wedge, and the volume of two cylinders' intersection. Although Archimedes made little use of differential calculus, He was similar to Newton in that he used his (non-rigorous) Calculus to discover results and then devise rigorous geometric proofs for publication. His original achievements in Physics include the principles of leverage, the first law of hydrostatics, and inventions like the compound pulley, the hydraulic screw, and war machines. Also, Archimedes discovered formula for the volume and surface area of a sphere, and may have been first to notice and prove the simple relationship between a circle's circumference and area. For these reasons, π is often called Archimedes' constant. His approximation 223/71 < π < 22/7 was the best of his day. (Apollonius soon surpassed it, but only by using Archimedes' method.)

In the 20th century, modern technology led to the discovery of new writings by Archimedes, hitherto hidden on a palimpsest. It included a note which may imply an understanding of the distinction between countable and uncountable infinities (a distinction which wasn't resolved until Georg Cantor, who lived 2300 years after the time of Archimedes). Although Newton may have been the most important mathematician, and Gauss the greatest theorem prover, it is widely accepted that Archimedes was the greatest genius who ever lived. Unfortunately, Archimedes was too far ahead of his time.

References

http://www.agnesscott.edu/lriddle/women/noether.htm

http://fabpedigree.com/james/greatmm.htm

Math Journal Test Anxiety

My highest anxiety about test taking is that I am going to fail. I have general anxiety disorder and for me it is a personal anxiety. I truly am my own worst enemy. I study hard and work hard but still have this fear. Since I have come back to school I have achieved a 4.0 GPA in all 4 semesters, but the anxiety is still there for every test.
   For me, it is even worse with papers and gets worse toward the end of the semester. I attempt to relieve this anxiety with ample studying. I tend to talk about my anxiety. Also, I listen to music before tests to calm myself, and try to turn what anxiety I have left into positive energy.
  Math tests tend to create equal test anxiety for me. I know with study I will understand what to do during the test, yet doubt my abilities. I also know from a non-anxious perspective, that I try my best in all I do. I am capable, and I can succeed. I just need to convince myself of that fact while I am anxious.

Math Journals 1 & 2

1st Journal
I. Rank your favorite subject (#1 = Favorite through #9 least favorite)
_7__Mathematics
_8__English
_1__Science
_2__Social Studies
_5__Art
_9__Business
_4__Computers
_3__Music
_6__Physical Education

II. How many math courses have you completed since you were in 8th grade?
(Count 9th grade as “one” and then continue from there.)

5

III. Write the name of your hometown and tell me how many miles your hometown is away from Fargo?

Fargo 0 miles away

IV. Math Autobiography and “Why do children learn math?”

Growing up math came fairly easy to me. I was in a math class all the way through my first year of college. I was in the advanced math path from seventh grade through 11th grade (pre-calculus). However, I did have a few hiccups along the way.
  My first issue with math was finishing what we called mad minutes. You had to answer 20-30 math problems depending on the chapter in less than one minute. These sheets created a lot of stress in my early life. I knew how to do all of the problems, but having a time limit scared me and I would freeze up. Eventually, with lots of practice at home, I was able to get past the freezing up and succeed.
  Geometry was another place I struggled. Learning all of the rules was my problem. It felt more like learning facts and memorization than doing math like I was used to. I did pass the class and move on but that year was very hard for me.
  Finally when I entered pre-calculus, which was half trigonometry half calculus, I realized I was in over my head. The teacher I had did not care if we did well or not, was not willing to help outside of class, and felt he was weeding us out and preventing failure in college. I did not grasp these concepts well and felt I had no place to turn. I switched from the advanced math course to the average track mid-year.
  I like learning math because it is a challenge. I enjoy solving problems and knowing I did well. The same reason I like math is the reason I dislike it. Sometimes it is too challenging for me and I get frustrated especially when I feel I have no one to turn to for help.
  I feel math is a necessity for life. We are constantly solving math problems in our daily lives. It may be paying for something with cash, or measuring an object to see if it will fit in a room. I still enjoy math, I do puzzles involving math problems from time to time, I just know my limits surrounding math.
  I feel children must learn math early. Math is like a foreign language. Young children learn language at a fast pace and so it makes sense to teach math during a time they are developing so quickly. I feel if we wait until children are older math actually would be harder to learn. Also, even at young ages math is crucial to life. It may be playing with Legos, buying candy, and many other situations. Math empowers children and helps them be more independent.