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Background, Introduction, Body and Future Work or Conclusion, where you first give the description of the problem history, including its key notions, then present the specific results of your study and then providing the possible direction of the future research in your field. The methodology of mathematics in not a subject that is widely studied, but still there exist several issues that could help to develop the methodology of your own research.

The first issue is the necessity to express complicated relations symbolically, which could help to master the notions that could hardly be expressed in words. The essential part of mathematics is abstraction that gives the possibility to codify out knowledge about several examples and thus to learn their common features.

The same importance has the rigorous notion of proof which makes mathematics applicable and essential in physics, engineering, computer science etc. Considering these several key points of a research, each writer should himself define the own research strategy. We have over expert writers with PhD and Masters level educations who are all ready to fulfill your writing needs, regardless of the academic level or research topic.

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We understand students have plenty on their plates, which is why we love to help them out. Let us do the work for you, so you have time to do what you want to do! Mathematics Research Paper Topics. The topics that deal with Homology Theories are the following: Unary and Binary Operations Research paper topics pertaining to Geometry: Euclidean Geometry Euclidean or elementary geometry is a geometric theory based on the system of axioms that was first stated by Euclid in the 3rd century BC.

Stereometry Stereometry is a branch of geometry that deals with the solid figures in space. Computational Geometry Computational Geometry is a branch of the discrete mathematics that deals with the algorithms for the solving of the geometric problems. Geometry algorithms Research paper topics on Calculus: Foundation and history of Calculus Calculus is a branch of mathematics that deals with the research of functions and their generalization by the methods of the differential and integral calculus.

Vector Spaces A vector space is a structure formed by vectors. Multivariate Calculus Multivariate calculus is differentiated and integrated calculus involving multiple variables. Research paper topics on Mathematical Logic: Model Theory Model theory is a branch of mathematical logics that deals with study of relations between the formal languages and their interpretations, or models. Set Theory Set theory is the branch of mathematics that deals with the general behavior of sets.

Recursion Theory Recursion theory, also called computability theory, is a branch of mathematical logic that is in close relation with computer science and deals with the study of computable functions and Turing degrees, including also the study of generalized computability and definability.

Proof Theory Proof theory is a branch of mathematical logics where the phenomenon of mathematical proof becomes an object of algebra or arithmetic. Probability and Statistics Topics: The topics that deal with the probability theory are the following: Conditional probability Probability distribution function 2. Statistical package comparison Research paper topics on Differential Equations: The essay will conclude with a section containing specific recommendations to consider as you write and rewrite the paper.

The purpose of nearly all writing is to communicate. In order to communicate well, you must consider both what you want to communicate, and to whom you hope to communicate it.

This is no less true for mathematical writing than for any other form of writing. The primary goal of mathematical writing is to assert, using carefully constructed logical deductions, the truth of a mathematical statement.

Careful mathematical readers do not assume that your work is well-founded; they must be convinced. This is your first goal in mathematical writing. However, convincing the reader of the simple truth of your work is not sufficient. When you write about your own mathematical research, you will have another goal, which includes these two; you want your reader to appreciate the beauty of the mathematics you have done, and to understand its importance.

If the whole of mathematics, or even the subfield in which you are working, is thought of as a large painting, then your research will necessarily constitute a relatively minuscule portion of the entire work. Its beauty is seen not only in the examination of the specific region which you have painted although this is important , but also by observing the way in which your own work 'fits' in the picture as a whole.

These two goals--to convince your reader of the truth of your deductions, and to allow your audience to see the beauty of your work in relation to the whole of mathematics--will be critical as you develop the outline for your paper. At times you may think of yourself as a travel guide, leading the reader through territory charted only by you. A successful mathematical writer will lay out for her readers two logical maps, one which displays the connections between her own work and the wide world of mathematics, and another which reveals the internal logical structure of her own work.

In order to advise your reader, you must first consider for yourself where your work is located on the map of mathematics. If your reader has visited nearby regions, then you would like to recall those experiences to his mind, so that he will be better able to understand what you have to add and to connect it to related mathematics. Asking several questions may help you discern the shape and location of your work: It is necessary that you explicitly consider this question of placement in the structure of mathematics, because it will linger in your readers' minds until you answer it.

Failure to address this very question will leave the reader feeling quite dissatisfied. In addition to providing a map to help your readers locate your work within the field of mathematics, you must also help them understand the internal organization of your work: Since your reader does not know what you will be proving until after he has read your paper, advising him beforehand about what he will read, just as the travel agent prepares his customer, will allow him to enjoy the trip more, and to understand more of the things you lead him to.

To honestly and deliberately explain where your work fits into the big picture of mathematical research may require a great deal of humility. You will likely despair that your accomplishments seem rather small. Mathematics has been accumulating for thousands of years, based on the work of thousands or millions of practitioners.

It has been said that even the best mathematicians rarely have more than one really outstanding idea during their lifetimes. It would be truly surprising if yours were to come as a high school student! Once you have considered the structure and relevance of your research, you are ready to outline your paper.

The accepted format for research papers is much less rigidly defined for mathematics than for many other scientific fields. You have the latitude to develop the outline in a way which is appropriate for your work in particular.

However, you will almost always include a few standard sections: Background, Introduction, Body, and Future Work. The background will serve to orient your reader, providing the first idea of where you will be leading him. In the background, you will give the most explicit description of the history of your problem, although hints and references may occur elsewhere. The reader hopes to have certain questions answered in this section: Why should he read this paper?

What is the point of this paper? Where did this problem come from? What was already known in this field? Why did this author think this question was interesting? If he dislikes partial differential equations, for example, he should be warned early on that he will encounter them. If he isn't familiar with the first concepts of probability, then he should be warned in advance if your paper depends on that understanding.

Remember at this point that although you may have spent hundreds of hours working on your problem, your reader wants to have all these questions answered clearly in a matter of minutes.

In the second section of your paper, the introduction, you will begin to lead the reader into your work in particular, zooming in from the big picture towards your specific results. This is the place to introduce the definitions and lemmas which are standard in the field, but which your readers may not know.

The body, which will be made up of several sections, contains most of your work. By the time you reach the final section, implications, you may be tired of your problem, but this section is critical to your readers. You, as the world expert on the topic of your paper, are in a unique situation to direct future research in your field. A reader who likes your paper may want to continue work in your field. If you were to continue working on this topic, what questions would you ask?

Also, for some papers, there may be important implications of your work. If you have worked on a mathematical model of a physical phenomenon, what are the consequences, in the physical world, of your mathematical work? These are the questions which your readers will hope to have answered in the final section of the paper. You should take care not to disappoint them! Formal and Informal Exposition. Once you have a basic outline for your paper, you should consider "the formal or logical structure consisting of definitions, theorems, and proofs, and the complementary informal or introductory material consisting of motivations, analogies, examples, and metamathematical explanations.

This division of the material should be conspicuously maintained in any mathematical presentation, because the nature of the subject requires above all else that the logical structure be clear. Thus, the next stage in the writing process may be to develop an outline of the logical structure of your paper. Graphs with few spanning substructures , Jessica De Silva. On the well-posedness and global boundary controllability of a nonlinear beam model , Jessie Jamieson.

High Cognitive Demand Examples in Precalculus: A Tensor's Torsion , Neil Steinburg. Adian inverse semigroups , Muhammad Inam. Homological characterizations of quasi-complete intersections , Jason M. Bridge spectra of cables of 2-bridge knots , Nicholas John Owad.

Stable local cohomology and cosupport , Peder Thompson. Graph centers, hypergraph degree sequences, and induced-saturation , Sarah Lynne Behrens. Systems of parameters and the Cohen-Macaulay property , Katharine Shultis. Betti sequences over local rings and connected sums of Gorenstein rings , Zheng Yang. Results on edge-colored graphs and pancyclicity , James Carraher. Well-posedness and stability of a semilinear Mindlin-Timoshenko plate model , Pei Pei.

Embedding and Nonembedding Results for R.

As of , International Mathematics Research Papers has been incorporated into International Mathematics Research Notices. Subscriptions to IMRP are no longer available. This site provides access to past issues of IMRP.

Mathematics Research Paper Topics Good Topics for Mathematics Research Papers A mathematics research paper is an extremely intricate task that requires immense concentration, planning and naturally clear basic knowledge of mathematics, but what is essential for a higher level research is the successful choice of a topic, matching your personal interests and level of competence.

Writing a Research Paper in Mathematics Ashley Reiter September 12, Section 1: Introduction: Why bother? Good mathematical writing, like good mathematics thinking, is a skill which must be practiced and developed for optimal performance. The purpose of this paper is to provide assistance for young mathematicians writing their first paper. Home > Mathematics > Dissertations, Theses, Research Papers. Mathematics, Department of Dissertations, Theses, and Student Research Papers in Mathematics. PhD candidates: You are welcome and encouraged to deposit your dissertation here, but be aware that 1) it is optional.

One Freelance Limited: a custom writing service that provides online custom-written papers, such as term papers, research papers, thesis papers, essays, dissertations, and other custom writing services inclusive of research materials for assistance purposes only. Journal of Mathematics Research This journal, published bimonthly (February, April, June, August, October and December) in both print and online versions, keeps readers up-to-date with the latest developments in all aspects of mathematics.