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❶Decision-Theoretic Analysis and Simulation Medical researchers and policy makers often face difficult decisions which require them to choose the best among two or more alternatives using whatever data are available. The proof itself marks a milestone in mathematics in that it is readily understandable, but impossible to check because it involves computer verification of an enormous number of special cases.
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We will never deny the fact that some topics are better than others and because of this, there is a need to choose the good ones against the bad ones when you want to write your thesis. Choosing the better topic has been one of the most difficult aspects of writing a thesis.

In fact, it is the major obstacle in the writing of a dissertation. However, there are some proactive ways through which you can select a good topic. Our services do not end in chemistry homework help , we also help you with choosing or selecting of good topics.

However, before you select good topics, you must know the things that make a good topic. There may be some subtle hidden attributes of a good topic which are not laid bare on the outside. These are the things you must search out for. Now, you should start looking at the end result expected of your thesis even when you are choosing the topic. The fact is that your examiners will want nothing but an original outcome.

Because of this, you should have a very good look at the research that is already done in the field to ensure that you are bringing something new.

In other words, essay topics must be novel and original. It is obvious that you may not find any entirely new idea which has not been studied before in the subject. What novelty in this sense means is that you should go for thesis topics that either emanated out of a combination of several ideas or the one that should be applied using a new method or the idea that will be used to solve a new problem. There must be something new and you must bring another angle to the works already done in the field.

When you want to ensure novelty in your work, you can go for an outcome that has never been achieved with the same process before. You can pick a specific niche and discover a problem that has not been addressed in the niche by any previous researchers.

You can also apply a new methodology in studying a subject that has been studied widely in the past. All these will surely give a new angle to the works. Even when we offer you admission essay writing service , there must be something new in each essay as against other previous essays before it. Another factor that must be inherent in any good research which we also observe when you buy research papers from us is the context.

Any new work you want to carry on must be put in context with research existing in the field. By so doing, you learn the methods other researchers used in unraveling the facts and ensure that nobody has done the exact thing you are doing. This will also help you to explain and clarify why your own research is also necessary.

Another attribute of good essay topics is that they must be topics you are competent to handle. Yes, you must ask yourself if you are experienced, skilled and handy enough to handle it. Check your resources and consider them side by side with the fact that an idea can be termed good only when you are able to execute and bring it to fulfillment, otherwise, it is of no use. When you have known the attributes of good thesis topics, you can now go ahead to choose a topic.

With the guidelines on what you are actually looking for, you can now start choosing. You don't have to sit down thinking and the idea will spring inside the mind. It is something that will take a gradual process. This process is one you can repeat severally before you come out with something perfect. The process involves idea generation, testing of the idea, elimination and then refinement. This is the method you should use in picking the topics when you need Marine Science homework help from us.

In the process of the idea generation, you should jettison the concept of searching for a perfect idea and imbibe the practice of considering many ideas to pick the right one.

Just be docile, knowing that ideas may not be perfect at first. With this, you will have time to look at the topics and see the great things you never considered in those topics. Just gather all of them and move to the next level. The next level is the testing of the ideas. You must remember that this part of the essay is among the most crucial parts.

You have to look at the ideas that will shape the essay and their availability, you have to check the possibility of the project being completed and how you can do the project. When you test each idea, try and do experiments and mini researches about them and see the information available.

Also ascertain if you will enjoy unhindered access to the information, people or the equipment needed, whether there are enough literature on this already, and others. You shouldn't ask, can you write my research paper , you should bring your research paper to be written. The testing will now lead you to the elimination and refinement where you sieve the ideas and let go of the ones that did not serve the purpose.

You should also go ahead to make amendments on the one chosen. You may even discover cases where entirely new ideas are drawn as a result of the findings from the draft thesis topics. The next is that the writer should struggle at all times to have the good data.

We offer the best writing and academic services and we work with good data. Even when we write your homework for you, they are all centered on good data. In what sense can one say that a product of infinitely many factors converges to a number? To what does it converge? Can one generalize the idea of n! This topic is closely related to a beautiful and powerful instrument called the Gamma Function.

Infinite products have recently been used to investigate the probability of eventual nuclear war. We're also interested in investigating whether prose styles of different authors can be distinguished by the computer.

Representation theory is one of the most fruitful and useful areas of mathematics. The development of the theory was carried on at the turn of the century by Frobenius as well as Shur and Burnside.

In fact there are some theorems for which only representation theoretic proofs are known. Representation theory also has wide and profound applications outside mathematics. Most notable of these are in chemistry and physics. A thesis in this area might restrict itself to linear representation of finite groups.

Here one only needs background in linear and abstract algebra. Lie groups are all around us. In fact unless you had a very unusual abstract algebra course the ONLY groups you know are Lie groups. Don't worry there are very important non-Lie groups out there. Lie group theory has had an enormous influence in all areas of mathematics and has proved to be an indispensable tool in physics and chemistry as well.

A thesis in this area would study manifold theory and the theory of matrix groups. The only prerequisites for this topic are calculus, linear and abstract algebra. One goal is the classification of some families of Lie groups. For further information, see David Dorman or Emily Proctor. The theory of quadratic forms introduced by Lagrange in the late 's and was formalized by Gauss in The ideas included are very simple yet quite profound.

One can show that any prime congruent to 1 modulo 4 can be represented but no prime congruent to 3 modulo r can. Of course, 2 can be represented as f 1,1. Let R n be the vector space of n-tuples of real numbers with the usual vector addition and scalar multiplication.

For what values of n can we multiply vectors to get a new element of R n? The answer depends on what mathematical properties we want the multiplication operation to satisfy. A thesis in this area would involve learning about the discoveries of these various "composition algebras" and studying the main theorems:.

Inequalities are fundamental tools used by many practicing mathematicians on a regular basis. This topic combines ideas of algebra, analysis, geometry, and number theory. We use inequalities to compare two numbers or two functions. These are examples of the types of relationships that could be investigated in a thesis. You could find different proofs of the inequality, research its history and find generalizations.

Hardy, Littlewood, and P—lya, Inequalities, Cambridge, Ramanujan or women in mathematics , the history of mathematics in a specific region of the world e.

Islamic, Chinese, or the development of mathematics in the U. Medical researchers and policy makers often face difficult decisions which require them to choose the best among two or more alternatives using whatever data are available. An axiomatic formulation of a decision problem uses loss functions, various decision criteria such as maximum likelihood and minimax, and Bayesian analysis to lead investigators to good decisions.

Foundations, Concepts and Methods, Springer-Verlag, The power of modern computers has made possible the analysis of complex data set using Bayesian models and hierarchical models. These models assume that the parameters of a model are themselves random variables and therefore that they have a probability distribution.

Bayesian models may begin with prior assumptions about these distributions, and may incorporate data from previous studies, as a starting point for inference based on current data. This project would investigate the conceptual and theoretical underpinnings of this approach, and compare it to the traditional tools of mathematical statistics as studied in Ma It could culminate in an application that uses real data to illustrate the power of the Bayesian approach.

Oxford University Press, New York. Bayesian Statistics for Evaluation Research: Measurements which arise from one or more categorical variables that define groups are often analyzed using ANOVA Analysis of Variance.

Linear models specify parameters that account for the differences among the groups. Sometimes these differences exhibit more variability than can be explained by these "fixed effects", and then the parameters are permitted to come from a random distribution, giving "random effects. This modeling approach has proved useful and powerful for analyzing multiple data sets that arise from different research teams in different places. For example the "meta-analysis" of data from medical research studies or from social science studies often employs random effects models.

This project would investigate random effects models and their applications. MA , with a plus. Because a computer is deterministic, it cannot generate truly random numbers. A thesis project could explore methods of generating pseudo-random numbers from a variety of discrete and continuous probability distributions.

The art of tilings has been studied a great deal, but the science of the designs is a relatively new field of mathematics. Some possible topics in this area are: The problems in this area are easy to state and understand, although not always easy to solve. The pictures are great and the history of tilings and patterns goes back to antiquity.

An example of a specific problem that a thesis might investigate is: Devise a scheme for the description and classification of all tilings by angle-regular hexagons.

Roughly speaking, a contraction of the plane is a transformation f: With a little effort CF can even be made to look like a tree or a flower!!

A thesis in this area would involve learning about these contraction mapping theorems in the plane and in other metric spaces, learning how the choice of contractions effects the shape of CF and possibly writing computer programs to generate CF from F. Consider a population of individuals which produce offspring of the same kind. Associating a probability distribution with the number of offspring an individual will produce in each generation gives rise to a stochastic i.

The earliest applications concerned the disappearance of "family names," as passed on from fathers to sons. Modern applications involve inheritance of genetic traits, propagation of jobs in a computer network, and particle decay in nuclear chain reactions. A key tool in the study of branching processes is the theory of generating functions, which is an interesting area of study in its own right.

Branching processes with biological applications. The Poisson Process is a fundamental building block for continuous time probability models. The process counts the number of "events" that occur during the time interval [0, T ], where the times between successive events are independent and have a common exponential distribution.

Incoming calls to a telephone switchboard, decays of radioactive particles, or student arrivals to the Proctor lunch line are all events that might be modeled in this way. Poisson processes in space rather than time have been used to model distributions of stars and galaxies, or positions of mutations along a chromosome.

Starting with characterizations of the Poisson process, a thesis might develop some of its important properties and applications.

Wiley, , Chapter 1. Two famous problems in elementary probability are the "Birthday Problem" and the "Coupon Collector's Problem.

For the second, imagine that each box of your favorite breakfast cereal contains a coupon bearing one of the letters "P", "R", "I", "Z" and "E". Now suppose that the "equally likely" assumptions are dropped. But how does one prove such claims? A thesis might investigate the theory of majorization, which provides important tools for establishing these and other inequalities. This is a modern topic combining ideas from probability and graph theory. A "cover time" is the expected time to visit all vertices when a random walk is performed on a connected graph.

Here is a simple example reported by Jay Emerson from his recent Ph. Consider a rook moving on a 2x2 chessboard. From any square on the board, the rook has two available moves. If the successive choices are made by tossing a coin, what is the expected number of moves until the rook has visited each square on the board? Reliability theory is concerned with computing the probability that a system, typically consisting of multiple components, will function properly e.

The components are subject to deterioration and failure effects, which are modeled as random processes, and the status of the system is determined in some way by the status of the components.

For example, a series system functions if and only if each component functions, whereas a parallel system functions if and only if at least one component functions. In more complicated systems, it is not easy to express system reliability exactly as a function of component reliabilities, and one seeks instead various bounds on performance. Specifically, in order to be Riemann integrable, a function must be continuous almost everywhere.

However, many interesting functions that show up as limits of integrable functions or even as derivatives do not enjoy this property. Certainly one would want at least every derivative to be integrable. To this end, Henri Lebesgue announced a new integral in that was completely divorced from the concept of continuity and instead depended on a concept referred to as measure theory.

Interesting in their own right, the theorems of measure theory lead to facinating and paradoxical insight into the structure of sets.

That is, we want a set of sets from F such that any two sets have a non-empty intersection. What is the structure of such a sub-collection? The conjecture remains open, though some particular cases have been solved.

For more information see John Schmitt Snark Hunting "We have sailed many months, we have sailed many weeks, Four weeks to the month you may mark , But never as yet 'tis your Captain who speaks Have we caught the least glimpse of a Snark! When Martin Gardner applied the name to a particular class of graphs in , a time when only four graphs including the Petersen graph of course were known to be in the class, it was an appropriate name.

Snarks were hunted by Bill Tutte while writing under the pseudonym Blanche Descartes as a way to approach the then unsolved Four Color Problem. They were both an elusive and worthy prey. Now there exists several infinite classes of snarks and they have proved to be useful, though not yet in the way Tutte envisioned.

Gardner , Penguin, Gardner, Mathematical games, Scientific American, , No. For more information see John Schmitt. Two-Dimensional Orbifolds Spheres and tori are examples of closed surfaces. There is a well-known classification theorem whereby we are able to completely characterize any surface based on only two pieces of information about the surface.

A 2-dimensional orbifold is a generalization of a surface. The main difference is that in general, an orbifold may have what are known as singular points.

A thesis in this area could examine Thurston's generalization of the surface classification theorem to 2-dimensional orbifolds. Another direction could be an examination of groups of transformations of the 2-dimensional plane which are used to produce flat 2-orbifolds. This subject is full of big ideas but can be pleasantly hands-on at the same time. For classification of 2-manifolds, see Wolf, p. Matrix Groups In linear algebra, we learn about n-by-n matrices and how they represent transformations of n-dimensional space.

In abstract algebra, we learn about how certain collections of n-by-n matrices form groups. These groups are very interesting in their own rights, both in understanding what geometric properties of n-dimensional space they preserve, and because of the fact that they are examples of objects known as manifolds. There are many senior projects that could grow out of this rich subject. See, for example, 27 above.

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.

These geometries are called non-Euclidean geometries, and include projective, hyperbolic, and spherical geometries. 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.

A thesis in this area would study the various geometries, and the groups of transformations that define them. David Gans, Transformations and Geometries. For further information, see Emily Proctor. Skip to main content. Site Editor Log On. For further information, see Bruce Peterson. The Four Color Theorem For many years, perhaps the most famous unsolved problem in mathematics asked whether every possible map on the surface of a sphere could be colored in such a way that any two adjacent countries were distinguishable using only four colors.

For additional information, see Bruce Peterson. Additive Number Theory We know a good deal about the multiplicative properties of the integers -- for example, every integer has a unique prime decomposition.

A thesis is an idea or theory that is expressed as a statement, a contention for which evidence is gathered and discussed logically. One of the most important concerns in choosing a thesis topic is that the topic speaks to an area of current or future demand.

Sep 01, · How to choose a thesis topic? Consider multiple options, do preliminary testing, and then refine good ideas, eliminate bad ones.

The last “if only” in the preceding list gives you an idea for a thesis, which you turn into a sentence: The emphasis on militarism in the training of the king’s men led to the tragic demise of Humpty Dumpty. You need to understand what is the main idea of your paper and how to communicate it in a comprehensive and concise way. Here are some of the thesis statement examples to help you make this task less problematic.

Included in this working thesis is a reason for the war and some idea of how the two sides disagreed over this reason. As you write the essay, you will probably begin to characterize these differences more precisely, and your working thesis may start to seem too vague. Mar 05, · What novelty in this sense means is that you should go for thesis topics that either emanated out of a combination of several ideas or the one that should be applied using a new method or the idea that will be used to solve a new problem/5(70).