Essay on Mathematics and Typical Mathematics Department

Submitted By sasssy23
Words: 631
Pages: 3
Open Document
Early one morning in the halls of a typical mathematics department, Katie, a graduate student in the field of higher category theory, walks into her final exam for grad algebra 1. She had enough sleep the previous night, and feels confident about her abilities. The first question is a routine application of Nakayama’s lemma, and the next an exercise in computing a group. After half an hour of deftly dealing out solutions, she comes to the last item:
Explain the importance of module theory in ring theory using a few examples.
What kind of exam is this? Katie thinks. The question is not true, false, a computation, a proof, or undecidable in ZFC + V=L! Madness!
The Role that Essays Could Have in Math

I made this story up entirely. However, believe incorporating a small amount of such questions would be useful in emphasising intuition and the aesthetic side of mathematics, and this is something that could be used in upper undergraduate and all graduate courses.

Don’t get me wrong; I think conventional mathematical problems are one of the most important parts of learning mathematics. However, there could be other aspects to a solid mathematical education besides problems and reading theorems. Personally I love to read solid, austere, and elegant math, but I also enjoy the informal atmosphere of attempting to explain intuition.
Thinking about the meaning or intuition behind concepts is vitally important. The true meaning of things cannot be ascribed a rigorous mathematical definition, but mathematicians are constantly using their own mental “picture” or intuition about their research to advance their field.
Having such vague questions in assignments would give students a chance to really think about the line of thought emphasised through intuitive sentiment. Moreover, students would be encouraged to express their intuition and aesthetic appreciation, and might find that although the final product of mathematics is and should be proof, it is also worthwhile to examine one’s subconscious driving force behind creative output. Moreover, vague questions do not have to have vague answers; a good answer I think would be a combination of vague intuitive statements with precise examples and statements of theorems that would motivate the topic of discussion.
I also feel that mathematics is a very beautiful subject, filled with vast scenes of the elegant and sometimes bizarre objects that come out of the deceptively simple axioms and ideas; this aesthetic feeling is something that should
Show More

Related Documents: Essay on Mathematics and Typical Mathematics Department

my career Essay

MY Career Mathematics is a subject that I enjoyed from a very young age, solving problems as identifying patterns has been one of my abilities of math. Is a career the interest me for my future. Mathematic is a discipline seed in the study of the all sciences. In addition to contributing to the development of nuclear energy, mathematicians played in important roles in the 20th century in the development of automobile, the television and space exploration. This on of the specialists in the…

Words 1475 - Pages 6

Three Prime Areas Analysis

youngest children, up to 3 years of age. At around the age of 3 years, as children become increasingly competent in the three prime areas, they need to build, develop and broaden their skills. The four specific areas aim to do this through literacy, mathematics, understanding the world, and expressive arts and design. Confidence in the prime areas will provide a platform for successful learning in these wide,…

Words 801 - Pages 4

Essay about Programmer Career Information

Facts - Computer Programmer: There were 426,000 computer programmers employed in 2008. Educational Requirements - Computer Programmer: To work as a computer programmer one must usually have a bachelor's degree, generally in computer science, mathematics, or information systems. Some computer programmers take coursework in computer science while earning their degrees in accounting, finance and business. Some of those working as computer programmers earn an associate's degree or certificate. Other…

Words 422 - Pages 2

Top Careers For People Haters

excel. Career #1: Accountant Find numbers and financial data more stimulating than small talk and conference calls? You might be a good fit in the often-isolated career of accountant. Why It's Great For Solitary Types: According to the U.S. Department of Labor, some primary responsibilities of an accountant may include computing taxes, preparing financial documents, and maintaining records - all tasks that won't require a lot of face-to-face interaction. "Although you can't avoid people entirely…

Words 1506 - Pages 7

Olga Case Study

taking notes. Often times she was unable to keep up with the rest of her class and was lost throughout the lecture. Due to this, her teachers often noted that she was daydreaming, and was not putting in the effort. Olga never asked for help in this department because she always wanted to blend in with her peers. Since she was unable to physically participate with them, she wanted to eliminate the barrier with her…

Words 1326 - Pages 6

Educational System in Nigeria Essay

important to note that some private schools offer GCE A-levels, which usually serve as a gap year after graduation for students that are interested. The common core curriculum at the senior secondary level consists of: English, one Nigerian language, mathematics, one science subject, one social science subject, and agricultural science or a vocational subject. In addition students must take three elective subjects, one of which may be dropped in the third year. Students take the Senior Secondary Certificate…

Words 2877 - Pages 12

Essay on No Child Left Behind Thesis

No Child Left Behind 1 Running head: NO CHILD LEFT BEHIND The Impact of the No Child Left Behind Act on the K-8 Setting Kara Robertson A Senior Thesis submitted in partial fulfillment of the requirements for graduation in the Honors Program Liberty University Fall 2009 No Child Left Behind 2 Acceptance of Senior Honors Thesis This Senior Honors Thesis is accepted in partial fulfillment of the requirements for graduation from the Honors Program of Liberty University…

Words 8350 - Pages 34

Essay on The Effectiveness of Technology in Schools

studies were chosen from an original set of over 1000; studies were excluded from the final set for such reasons as methodological weakness (e.g., lack of alternative treatments in comparative studies) and focus on extraneous issues (e.g., critiques of typical research methods, research on the attitudes of student teachers, research on the physical layout of technology-rich classrooms). Seventy of the final set appeared in professional journals, while 33 were doctoral dissertations. The report itself…

Words 5921 - Pages 24

Essay High School and Peer School Percentile

State of New Jersey 11-5390-050 VINELAND HIGH 2880 E CHESTNUT AVE VINELAND, NJ 08360-6144 OVERVIEW CUMBERLAND VINELAND CITY GRADE SPAN 09-12 This school's academic performance significantly lags in comparison to schools across the state. Additionally, its academic performance lags in comparison to its peers. This school's college and career readiness lags in comparison to schools across the state. Additionally, its college and career readiness lags in comparison to its peers. This school's graduation…

Words 3850 - Pages 16

Essay about Strategic Restructuring

Restructuring: Operations and Engineering Jason AlexanderBUS340: Business Communications Instructor: Andrea Robinson 8/12/13 EXECUTIVE SUMMARY In this business proposal, it will be recommended to change the way the Operations and Engineering departments interface at the Easterling Munitions Factory (EMF). Currently, there are six operational supervisors – one for each part of the manufacturing process – along with three engineers – a chemical engineer, a manufacturing engineer, and a mechanical…

Words 1709 - Pages 7