Senior Thesis Topic in Number Theory

In summary, the person is looking for a topic for their senior thesis in mathematics, specifically in Number Theory. They have a background in senior level math courses and have done a research paper on the Collatz Conjecture in the past. They are seeking suggestions on a topic that is both beautiful and interesting. Some potential topics could be the theory of continued fractions, the Pell equation, or the theory of quadratic forms. Each of these topics have various interesting aspects to explore, such as properties, theorems, and applications.
  • #1
IAmAbelian
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As the title suggests, I am looking for a topic to do my senior thesis on. It doesn't have to be original work, but it does have to be rather math intensive. Also, I have to do it on a topic in Number Theory for reasons beyond my control. I have the typical senior level background(e.g. Modern Algebra, Topology, Complex and Real Analysis, etc.) and I have also taken a class in Number Theory. I have done a research paper in the past(for a different mathematics course) on the Collatz Conjecture, but I really don't want to try to write a 15-20 page paper on that(which is the relative length required of my thesis).

I would greatly appreciate any input anyone can offer on the matter, as I really want to do my thesis on a subject which I find beautiful and interesting. Thanks!
 
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  • #2
One possible topic is the theory of continued fractions. There are many interesting topics to explore in this field, such as the properties and behavior of continued fractions, theorems about approximations of irrational numbers by rationals, and the relationship between algebraic numbers and continued fractions. You could also look into topics related to the Pell equation, which is closely related to continued fractions, and involves some interesting number theoretic concepts. Another option is the theory of quadratic forms. This involves the study of certain types of polynomials in two or more variables, particularly those that are quadratic in each variable. Here you could investigate topics such as the classification of quadratic forms, the representation of primes using quadratic forms, and the local-global principle for quadratic forms.
 

Related to Senior Thesis Topic in Number Theory

1. What is a senior thesis topic in number theory?

A senior thesis topic in number theory is a research project that focuses on studying properties and patterns of numbers, such as prime numbers, perfect numbers, and irrational numbers. It typically involves proving or disproving conjectures and exploring connections between different areas of number theory.

2. How do I choose a senior thesis topic in number theory?

Choosing a senior thesis topic in number theory can be a challenging task. It is important to find a topic that interests you and that you have a strong foundation in. You can also discuss potential topics with your advisor and do some preliminary research to identify a topic that has not been extensively studied yet.

3. What skills are necessary for a senior thesis topic in number theory?

A strong background in mathematical concepts such as algebra, geometry, and calculus is necessary for a senior thesis topic in number theory. Additionally, skills in critical thinking, problem-solving, and proof writing are important for successfully completing a number theory research project.

4. What are some potential applications of a senior thesis topic in number theory?

Number theory has many real-world applications, including cryptography, coding theory, and computer science. A senior thesis topic in number theory can also lead to advancements in other areas of mathematics, such as algebraic geometry and topology.

5. How long does it take to complete a senior thesis topic in number theory?

The length of time it takes to complete a senior thesis topic in number theory can vary depending on the complexity of the topic and the amount of research and analysis required. On average, it can take anywhere from 6 months to a year to complete a senior thesis in number theory.

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