thesis linear

phd thesis work plan

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Thesis linear foundation degree essays

Thesis linear

Because I was on the flow of writing results in the social sciences field, I agreed with my supervisors to keep the flow and start the thesis writing from the results chapters. At this stage both chapters 5 and 6 need some revisions, but nothing really major. I believe that in 2 weeks roughly one week for each all the needed amendments can be done. Next step is to go back to Chapter 2 — Literature Review and Theoretical Framework — then chapters 3, 4, 1 and 8! A mess I know, but introduction and conclusion are outlined and although every now and then I go back there to make some notes, my intent is to write them properly when all the other chapters are finished.

The goal for the next 50 days is to finish — at least! But right now it feels so good to have Chapter 7 out of my hands for the next week! How is your writing schedule? Are you in a linear — from chapter 1 to the end — or in a non-linear process? My thesis for my Ph. Hi Sharon. I guess it is related to the kind of writing, you are right. When writing my Masters dissertation I wrote from beginning to the end as well, and that was in science so more straight forward than this thesis I am writing at the moment.

For this project I do think it has been working this way, and I hope these 3 chapters I — sort of — finished were the most complex ones! Thanks for your comment! You are commenting using your WordPress. You are commenting using your Google account. You are commenting using your Twitter account.

You are commenting using your Facebook account. Notify me of new comments via email. Notify me of new posts via email. This site uses Akismet to reduce spam. Learn how your comment data is processed. Thesis writing: a linear or non-linear process? Advisor: McKinney, Earl H. Date: Type: Undergraduate senior honors thesis. Archival ID: A Degree: Thesis B.?.

Department: Honors College. Abstract: This thesis discusses the basic problems of solving a linear programming problem. A definition of the linear programming problem is stated. Basic linear algebra methods are necessary to solve a linear programming LP problem. A short synopsis of the necessary methods used are presented, including examples. The simplex algorithm is introduced and an example is used to demonstrate its applicability.

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At this stage both chapters 5 and 6 need some revisions, but nothing really major. I believe that in 2 weeks roughly one week for each all the needed amendments can be done. Next step is to go back to Chapter 2 — Literature Review and Theoretical Framework — then chapters 3, 4, 1 and 8!

A mess I know, but introduction and conclusion are outlined and although every now and then I go back there to make some notes, my intent is to write them properly when all the other chapters are finished. The goal for the next 50 days is to finish — at least! But right now it feels so good to have Chapter 7 out of my hands for the next week! How is your writing schedule? Are you in a linear — from chapter 1 to the end — or in a non-linear process?

My thesis for my Ph. Hi Sharon. I guess it is related to the kind of writing, you are right. When writing my Masters dissertation I wrote from beginning to the end as well, and that was in science so more straight forward than this thesis I am writing at the moment.

For this project I do think it has been working this way, and I hope these 3 chapters I — sort of — finished were the most complex ones! Thanks for your comment! You are commenting using your WordPress. You are commenting using your Google account. You are commenting using your Twitter account. You are commenting using your Facebook account. Notify me of new comments via email. Notify me of new posts via email. This site uses Akismet to reduce spam. Learn how your comment data is processed.

Thesis writing: a linear or non-linear process? These three chapters present the main results of my research: Chapter 5 is the results based upon the case study sites and highly based on participant observation. Quantum computing promises a new paradigm of computation where information is processed in a way that has no classical analogue.

There are a number of physical platforms conducive to quantum computation, each with a number of advantages and challenges. Single photons, manipulated using integrated linear optics, constitute a promising platform for universal quantum computation. Their low decoherence rates make them particularly favourable, however the inability to perform deterministic two-qubit gates and the issue of photon loss are challenges that need to be overcome. In this thesis we explore the construction of a linear optical quantum computer based on the cluster state model.

We identify the different necessary stages: state preparation, cluster state construction and implementation of quantum error correcting codes, and address the challenges that arise in each of these stages. For the state preparation, we propose a series of linear optical circuits for the generation of small entangled states, assessing their performance under different scenarios.

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Next step is to go back to Chapter 2 — Literature Review and Theoretical Framework — then chapters 3, 4, 1 and 8! A mess I know, but introduction and conclusion are outlined and although every now and then I go back there to make some notes, my intent is to write them properly when all the other chapters are finished.

The goal for the next 50 days is to finish — at least! But right now it feels so good to have Chapter 7 out of my hands for the next week! How is your writing schedule? Are you in a linear — from chapter 1 to the end — or in a non-linear process? My thesis for my Ph.

Hi Sharon. I guess it is related to the kind of writing, you are right. When writing my Masters dissertation I wrote from beginning to the end as well, and that was in science so more straight forward than this thesis I am writing at the moment.

For this project I do think it has been working this way, and I hope these 3 chapters I — sort of — finished were the most complex ones! Thanks for your comment! You are commenting using your WordPress. You are commenting using your Google account. You are commenting using your Twitter account. You are commenting using your Facebook account. Notify me of new comments via email. Notify me of new posts via email. This site uses Akismet to reduce spam.

Learn how your comment data is processed. Thesis writing: a linear or non-linear process? These three chapters present the main results of my research: Chapter 5 is the results based upon the case study sites and highly based on participant observation. This chapter is also very descriptive of what I have seen in the sites and what was said in the interviews with key informants.

Chapters 6 and 7 were one chapter to start with, but ended up being split in two. The thesis would not involve computer work. We know a good deal about the multiplicative properties of the integers -- for example, every integer has a unique prime decomposition. For instance, in how many ways can we write an integer as the sum of two squares?

How many ways can we write the number 1 as the sum of three cubes? Is every number the sum of two primes Goldbach's conjecture? This theorem has recently been proved by Andrew Wiles of Princeton University. References: T. Numbers like 6 and 28 were called perfect by Greek mathematicians and numerologists since they are equal to the sum of their proper divisors e.

Since then about B. Consequently, some mathematicians have tried to determine the values of p for which 2p-1 is prime. There still remain many open questions, for example, do there exist any odd perfect numbers? Research could include some interesting computer work if desired. Reference: T. Recent results indicate that any "reasonable" voting procedure must either be dictatorial or subject to strategic manipulation.

Many "possibility" theorems have been proved for voting mechanisms which satisfy relaxed versions of Arrow's axioms. How does one fit this model to real data? Are there other meaningful extensions of the logistic model? How are the Lotka-Volterra models of competition and predation affected by the assumption that one species grows logistically in the absence of the other?

A typical problem in this field would ask how to maximize the present value of discounted net economic revenue associated with the hunting and capture of whales. How does an optimal strategy vary with the number of competing whaling fleets? In , a Dutch mathematician L E. In recent years, new and simpler existence proofs of the fixed point theorem have been discovered. There has also been much progress on the problem of computationally determining fixed points.

Here N is the number of tumor cells at time t, K is the largest tumor size and b is a positive constant. A thesis in this area would begin with an investigation of the mathematical properties of this model and the statistical tests for deciding when it is a good one. The thesis would then move to a consideration of stochastic models of the tumor growth process. Reference: B. Hanson and C. Most defense spending and planning is determined by assessments of the conventional ie. The dynamic nature of warfare has historically been modelled by a particular simple linked system of differential equations first studied by F.

Lanchester Models of Warfare. The Fundamental Theorem of Algebra states that every non-constant polynomial with complex coefficients has a complex root. Gauss was the first person to give a proof of this result; in fact, he discovered four different proofs. All known proofs require some complex analysis.

However, the theorem is one of algebra and a purely algebraic proof would be nice to find. Emil Artin has given one that's almost purely algebraic. References: Any text in complex analysis. J Munkres, An Introduction to Topology. Serge Lang, Algebra for Artin's proof. A real number r is "algebraic" if r is the root of a polynomial with integer coefficients.

Thus every rational number is algebraic as are many of the more familiar irrational numbers such as the square root of 2 and the l7th root of 3. Liouville was the first to show explicitly that a certain number was not algebraic. Later in the l9th Century, proofs were discovered that e and pi are not algebraic.

All these proofs are within the grasp of a senior mathematics major. Reference: W. Would you like to see epsilons and deltas returned to Greek , where they belong? Your beginning calculus teachers only pay lip service to them anyway, fudging the definition of limit through phrases like "a tiny bit away" or "as close as you please. In some ways it leaps back in time past the 19th Century godfathers of modern analysis to the founders of calculus by introducing, but in a rigorous way, "infinitesimals" into the real number system.

Mathematics is not a static, immutable body of knowledge. New approaches to old problems are constantly being investigated and, if found promising, developed. Nonstandard analysis is a good and exciting example of this mathematical fact of life.

References: A. Robinson, Non-standard Analysis H Jerome Keisler, Elementary Calculus The relation between fields, vector spaces, polynomials, and groups was exploited by Galois to give a beautiful characterization of the automorphisms of fields. From this work came the proof that a general solution for fifth degree polynomial equations does not exist. Along the way it will be possible to touch on other topics such as the impossibility of trisecting an arbitrary angle with straight edge and compass or the proof that the number e is transcendental.

Mathematicians since antiquity have tried to find order in the apparent irregular distribution of prime numbers. Let PI x be the number of primes not exceeding x. Many of the greatest mathematicians of the 19th Century attempted to prove this result and in so doing developed the theory of functions of a complex variable to a very high degree.

Partial results were obtained by Chebyshev in and Riemann in , but the Prime Number Theorem as it is now called remained a conjecture until Hadamard and de la Valle' Poussin independently and simultaneously proved it in However, Hilbert's proof did not determine the numerical value of g k for any k. Peter Schumer, Introduction to Number Theory. Primes like 3 and 5 or and are called twin primes since their difference is only 2.

It is unknown whether or not there are infinitely many twin primes. In , Leonard Euler showed that the series S extended over all primes diverges; this gives an analytic proof that there are infinitely many primes. However, in Viggo Brun proved the following: if q runs through the series of twin primes, then S converges.

Hence most primes are not twin primes. A computer search for large twin primes could be fun too. Reference: E. Landau, Elementary Number Theory, Chelsea, ; pp. Do numbers like make any sense? The above are examples of infinite continued fractions in fact, x is the positive square root of 2. Moreover, their theory is intimately related to the solution of Diophantine equations, Farey fractions, and the approximation of irrationals by rational numbers.

References: L. Homrighausen, "Continued Fractions", Senior Thesis, One such area originated with the work of the Russian mathematician Schnirelmann. He proved that there is a finite number k so that all integers are the sum of at most k primes. Subsequent work has centered upon results with bases other than primes, determining effective values for k, and studying how sparse a set can be and still generate the integers -- the theory of essential components.

This topic involves simply determining whether a given integer n is prime or composite, and if composite, determining its prime factorization. Checking all trial divisors less than the square root of n suffices but it is clearly totally impractical for large n.

Why did Euler initially think that 1,, was prime before rectifying his mistake? Analytic number theory involves applying calculus and complex analysis to the study of the integers. Its origins date back to Euler's proof of the infinitude of primes , Dirichlet's proof of infinitely many primes in an arithmetic progression , and Vinogradov's theorem that all sufficiently large odd integers are the sum of three primes Did you spot the arithmetic progression in the sentence above?

A finite field is, naturally, a field with finitely many elements. Are there other types of finite fields? Are there different ways of representing their elements and operations? 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. Reference: Curtis, Matrix 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. There are many topics in the history of mathematics that could be developed into a thesis -- the history of an individual or group of mathematicians e.

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. To compare these approaches to the more traditional Neyman-Pearson Hypotheses testing, computer simulation using massive resampling MA or its equivalent provide the needed background. Emerson, J. 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.

References: Gelman, A. Bayesian Statistics: An Introduction. Oxford University Press, New York. Pollard, William E. 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. A simulation project could illustrate the properties and the strengths of the models when used for making inferences. References: Emerson, J. Hoaglin, D. Mosteller, and J. Tukey, Eds.