100+ Amazing Algebra Topics for Research Papers

Algebra Topics

Many students seek algebra topics when writing research papers in this mathematical field. Algebra is the study field that entails studying mathematical symbols and rules for their manipulation. Algebra is the unifying thread for most mathematics, including solving elementary equations to learning abstractions like rings, groups, and fields.

In most cases, people use algebra when unsure about the exact numbers. Therefore, they replace those numbers with letters. In business, algebra helps with sales prediction. While many students dislike mathematics, avoiding algebra research paper topics is almost impossible at an advanced study level.

Therefore, this article lists topics to consider when writing a research paper in this academic field. It’s helpful because many learners struggle to find suitable topics when writing research papers in this field.

How to Write Theses on Advanced Algebra Topics

A thesis on an algebra topic is an individual project that the learner writes after investigating and studying a specific idea. Here’s a step-by-step guide for writing a thesis on an algebra topic.

  1. Pick a topic: Start by selecting a title for your algebra thesis. Your topic should relate to your research interests and your supervisor’s guidelines.
  2. Investigate your topic: Once you’ve chosen a topic, research it extensively to know the relevant theories, formulas, and texts. Your thesis should be an extension of a particular topic’s analysis and a report on your research.
  3. Write the thesis: Once you’ve explored the topic extensively, start writing your paper. Your dissertation should have an abstract, an introduction, the body, and a conclusion.

The abstract should summarise your thesis’ aims, scope, and conclusions. The introduction should introduce the topic, size, and significance while providing relevant literature and outlining the logical structure. The body should have several chapters with details and proofs of numerical implementations, while the conclusion should restate your main arguments and tell readers the effects. Also, it should suggest future work.

College Algebra Topics

You may need topics to consider if you’re in college and want to write an algebra research paper. Here’s a list of titles worth considering for your essay.

  1. Exploring the relationship between Rubik’s cube and the group theory
  2. Comparing the relationship between various equation systems
  3. Finding the most appropriate way to solve mathematical word problems
  4. Investigating the distance formula and its origin
  5. Exploring the things you can achieve with determinants
  6. Explaining what “domain” and “range” mean in algebra
  7. A two-dimension analysis of the Gram-Schmidt process
  8. Exploring the differences between eigenvalues and eigenvectors
  9. What the Cramer’s rule states, and why does it matter
  10. Describing the Gaussian elimination
  11. Provide an induction-proof example
  12. Describe the uses of F-algebras
  13. Understanding the number problems in algebra
  14. What’s the essence of abstract algebra?
  15. Investigating Fermat’s last theorem peculiarities
  16. Exploring the algebra essentials
  17. Investigating the relationship between geometry and algebra

These are exciting topics in college algebra. However, writing a winning paper about any of them requires careful research and analysis. Therefore, prepare to spend sufficient time working on any of these titles.

Cool Topics in Algebra

Perhaps, you want to write about an excellent topic in this mathematical field. If so, consider the following ideas for your algebra paper.

  1. Discussing a differential equation with illustrations
  2. Describing and analysing the Noetherian ring
  3. Explain the commutative ring from an algebra viewpoint
  4. Describe the Artin-Weddderburn theorem
  5. Studying the Jacobson density theorem
  6. Describe the four properties of any binary operation from an algebra viewpoint
  7. A detailed analysis of the unary operator
  8. Analysing the Abel-Ruffini theorem
  9. Monomorphisms versus Epimorphisms: Contrast and comparison
  10. Discus Morita duality with algebraic structures in mind
  11. Nilpotent versus Idempotent in Ring theory

Pick any idea from this list and develop it into a research topic. Your educator will love your paper and award you a good grade if you research it and write an informative essay.

Linear Algebra Topics

Linear algebra covers vector spaces and the linear mapping between them. Linear equation systems have unknowns, and mathematicians use vectors and matrices to represent them. Here are exciting topics in linear algebra to consider for your research paper.

  1. Decomposition of singular value
  2. Investigating linear independence and dependence
  3. Exploring projections in linear algebra
  4. What are linear transformations in linear algebra?
  5. Describe positive definite matrices
  6. What are orthogonal matrices?
  7. Describe Euclidean vector spaces with examples
  8. Explain how you can solve equation systems with matrices
  9. Determinants versus matrix inverses
  10. Describe mathematical operations using matrices
  11. Functional analysis of linear algebra
  12. Exploring linear algebra and its fundamentals

These are some of the exciting project topics in linear algebra. Nevertheless, prepare sufficient resources and time to investigate any of these titles to write a winning paper.

Pre Algebra Topics

Are you interested in a pre-algebra research topic? If so, this category has some of the most exciting ideas to explore.

  1. Investigating the importance of pre-algebra
  2. The best way to start pre-algebra for a beginner
  3. Pre-algebra and algebra- Which is the hardest and why?
  4. Core lessons in pre-algebra
  5. What follows pre-algebra?
  6. The first things to learn in pre-algebra
  7. Investigating the standard form in pre-algebra
  8. Provide pre-algebra examples using the basic rules to evaluate expressions
  9. Differentiate pre-algebra and algebra
  10. Describe five pre-algebra formulas

Consider exploring any of these ideas if you’re interested in pre-algebra. Nevertheless, choose a title you’re comfortable with to develop a winning paper.

Intermediate Algebra Topics for Research

Perhaps, you’re interested in intermediate algebra. If so, consider any of these ideas for your research paper.

  1. Reviewing absolute value and real numbers
  2. Investigating real numbers’ operations
  3. Exploring the cube and square roots of real numbers
  4. Analysing algebraic formulas and expressions
  5. What are the rules of scientific notation and exponents?
  6. How to solve a linear inequality with a single variable
  7. Exploring relations, functions, and graphics from an algebraic viewpoint
  8. Investigating linear systems with two variables and solutions
  9. How to solve a linear system with two variables
  10. Exploring linear systems applications with two variables
  11. How to solve a linear system with three variables
  12. Gaussian elimination and matrices
  13. How to simplify a radical expression
  14. How to add and subtract a radical expression
  15. How to multiply and divide a radical expression
  16. How to extract a square root and complete the square
  17. Investigating quadratic functions and graphs
  18. How to solve a polynomial and rational inequality
  19. How to solve logarithmic and exponential equations
  20. Exploring arithmetic series and sequences

These are exciting topics in intermediate algebra to consider for research papers. Nevertheless, learners should prepare to solve equations in their work.

Algebra Topics High School Students Can Explore

Are you in high school and want to explore algebra? If yes, consider these topics for your research, they could be a great coursework help to you.

  1. Crucial principles and formulas to embrace when solving a matrix
  2. Ways to create charts on a firm’s financial analysis for the past five years
  3. How to find solutions to finance and mathematical gaps
  4. Ways to solve linear equations
  5. What is a linear equation- Provide examples
  6. Describe the substitution and elimination methods for solving equations
  7. How to solve logarithmic equations
  8. How to simplify a radical expression
  9. What are partial fractions?
  10. Describe linear inequalities with examples
  11. How to solve a quadratic equation by factoring
  12. How to solve a quadratic equation by formula
  13. How to solve a quadratic equation with a square completion method
  14. How to frame a worksheet for a quadratic equation
  15. Explain the relationship between roots and coefficients
  16. Describe rational expressions and ways to simplify them
  17. Describe a cubic equation roots
  18. What is the greatest common factor- Provide examples
  19. What is the least common multiple- Provide examples
  20. Describe the remainder theorem with examples

Explore any of these titles for your high school paper. However, pick a title you’re comfortable working with from the beginning to the end to make your work easier.

Advanced Topics in Algebra and Geometry

Maybe you want to explore something more advanced in your paper. In that case, the following list has advanced topics in geometry and algebra worth considering.

  1. Arithmetical structures and their algorithmic aspects
  2. Fractional thermoentropy spaces in topological quantum fields
  3. Fractional thermoentripy spaces in large-scale systems
  4. Eigenpoints configurations
  5. Investigating the higher dimension aperiodic domino problem
  6. Exploring math anxiety, executive functions, and math performance
  7. Coherent quantiles and lifting elements
  8. Absolute values extension on two subfields
  9. Reviewing the laws of form and Majorana fermions
  10. Studying the specialisation and rational maps degree
  11. Investigating mathematical-pedagogical knowledge of prospective teachers in ECD programs
  12. The adeles I model theory
  13. Exploring logarithmic vector fields, arrangements, and divisors’ freeness
  14. How to reconstruct curves from Hodge classes
  15. Investigating Eigen points configuration

These are advanced topics in algebra and geometry worth investigating. However, please prepare to explore your topic extensively to write a strong essay.

Abstract Algebra Topics

Most people study abstract algebra in college. If you’re interested in research in this area, consider these topics for your project.

  1. Describe abstract algebra applications
  2. Why is abstract algebra essential?
  3. Describe ring theory and its application
  4. What is group theory, and why does it matter?
  5. Describe the critical conceptual algebra levels
  6. Describe the fundamental theorem of the finite Abelian groups
  7. Describe Sylow’s theorems
  8. What is Polya counting?
  9. Describe the RSA algorithm
  10. What are the homomorphisms and ideals of Rings?
  11. Describe integral domains and factorisation
  12. Describe Boolean algebra and its importance
  13. State and explain Cauchy’s Theorem- Why is it important?

This algebra topics list is not exhaustive. You can find more ideas worth exploring in your project. Nevertheless, pick an idea you will work with comfortably to deliver a winning paper.

Get Professional Math Homework Help!

Perhaps, you don’t have the time to find accurate algebra homework solutions. Maybe you need math thesis help from an expert. If so, you’ve no reason to search further. Our thesis writing services in USA can help you write a winning assignment. We offer custom help with math assignments at cheap prices.

If you want to get a quality algebra dissertation without sweating, place an order with us. We’re an online team providing homework help to students across educational levels. We guarantee you a top-notch service once you approach us, saying, “Please do my math assignment.” We’re fast and can beat even a tight deadline without compromising quality. And whether you’re in high school, university, or college, we will write a paper that will compel your teacher to award you the best grade in your class. Contact us now!

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