Since that time the research in representation theory has been extremely active and its applications to all areas of mathematics has been very fruitful. In the late 19th century, geometry was revolutionized by the realization that if Euclid's fifth axiom, the parallel postulate, was dropped, there were a number of alternate geometries that satisfied the first four axioms but that displayed behavior quite different from traditional Euclidean geometry. For some students this provides a golden opportunity to move to a more professional level of work in their chosen field. Unlike with other companies, you'll be working directly with your writer without agents or intermediaries, which results in lower prices. Only the generosity and vision of those who give to Carthage make this possible. There still remain many open questions, for example, do there exist any odd perfect numbers? A typical question one might ask is give a fixed quadratic form, what integers, n , can such a form represent.
The short- and long-term benefits from writing a thesis are available to everyone and not just those going to law school or graduate school. For further information, see Mike Olinick. Pseudo-Random Number Generation Because a computer is deterministic, it cannot generate truly random numbers. Good senior theses require multiple drafts, with serious revisions being made based on the comments of your adviser. It is something that will take a gradual process. A thesis might investigate the theory of majorization, which provides important tools for establishing these and other inequalities.
Mathematicians have developed very sophisticated methods to deal with this problem. Choosing the better topic has been one of the most difficult aspects of writing a thesis. The development of the theory was carried on at the turn of the century by Frobenius as well as Shur and Burnside. Some possible topics in this area are: symmetry, topology, transitivity, tilings using only certain shapes, or tiles with special characteristics, classification of patterns, colorings, and geometry. References: Hardy, Littlewood, and P—lya, Inequalities, Cambridge, 1952. It is not a common topic, but for sure it is a fascinating one. Don't worry there are very important non-Lie groups out there.
The first step to developing an interesting research paper is choosing a good topic. Just talking about a topic you like usually nets a descriptive report, not an analytical paper—and reports come in on the lowest rung of the intellectual food chain. In more formal language, this asks for the cover time for the cyclic graph C4. The Senior Thesis, a long running program, has been replaced by. Nevertheless, do not let your research paper assignment give you anxiety and influence your overall studies. Is every number the sum of two primes Goldbach's conjecture? What is the structure of such a sub-collection? Poisson processes in space rather than time have been used to model distributions of stars and galaxies, or positions of mutations along a chromosome. Reference: Davenport, The Higher Arithmetic.
Additive Bases Attempts to prove Goldbach's Conjecture have led to the development of new areas in additive number theory see Additive Number Theory, topic 3. As the theory of these geometries began to develop, one of the great mathematicians of the day, Felix Klein, proposed his Erlangen Program, a new method for studying and characterizing these geometries based on group theory and symmetries. Finding the Right Research Paper Topic If you are in a class that allows you to choose your own term paper topic, there are some important areas to consider before you begin your project: Your Level of Interest: Research papers are time-consuming; you will be spending countless hours researching the topic and related topics, developing several primary and secondary sources, and putting everything together into a paper that is coherent and accomplishes your objectives. It would be easier to explore the theme and write about it. This result, a fundamental theorem in topology, has also had many applications in economics and the theory of games. The year-long course History 99 requires intensive research in primary sources and culminates in a major piece of writing usually 60 to 100 pages. But, in many cases, the most successful projects are expansions, reworkings, and further explorations of previous course papers.
Is it difficult finding employment? It is unknown whether or not there are infinitely many twin primes. This will also help you to explain and clarify why your own research is also necessary. Bayesian Data Analysis Lee, Peter M. The final thesis is due in April on a specific date set by the department, normally after the second spring vacation. Curtis, Matrix Groups For further information, see Emily Proctor. Paul Ribenbaum, 13 Lectures on Fermat's Last Theorem, Springer-Verlag, 1979.
J Munkres, An Introduction to Topology. Another direction could be an examination of groups of transformations of the 2-dimensional plane which are used to produce flat 2-orbifolds. Interesting in their own right, the theorems of measure theory lead to facinating and paradoxical insight into the structure of sets. References: Joel Franklin, Methods of Mathematical Economics. A senior thesis project could include a presentation of several different types of proof and a search for an algebraic one.
It is essential that you get feedback from readers you respect at every stage of proposal development. We recommend selecting a controversial topic, that will be easy to research and in which you can include your own insights and opinions. For example, a student who is immersed in the arts or music at school may choose to write about funding for music and art programs in elementary and secondary education or music piracy and copyright laws. Are external factors entirely to blame? The Arithmetic-Geometric Inequality and Other Famous Inequalities Inequalities are fundamental tools used by many practicing mathematicians on a regular basis. This makes it easier to write about and research as well as contributing personal knowledge to the subject. A computer search for large twin primes could be fun too. If you a potential advisor in mind, that person may well have other ideas.
Galois Theory The relation between fields, vector spaces, polynomials, and groups was exploited by Galois to give a beautiful characterization of the automorphisms of fields. Many students develop a relationship with faculty who then recommend them for admission to law school or graduate school. Surprisingly, people can be addicted to ordinary things, like sugar and salt. You cannot add watery text about anything into the paper. You may even discover cases where entirely new ideas are drawn as a result of the findings from the draft thesis topics. Interesting and Funny Research Paper Topics You may also want to base your research paper on something interesting or funny, which is not new.
If not, you should immediately begin seeking out a faculty member who does work in your area of interest. You can't really play unless you know your position and who else is playing. Ross, Introduction to Probability Models Academic Press, 1993 , Chapter 9. Professional Credentials: Completion of a thesis is an important credential for law school, graduate school, and employment. A graduate student will write a high school essay with great ease, while the reverse will result in a lot of difficulties on the part of the student. In what sense can one say that a product of infinitely many factors converges to a number? For related ideas, see Waring's Problem topic 22.