15 PhD Thesis Topics In Mathematics That Are Rather Challenging

Mathematics on its own can be a challenging topic, and if not blessed with strong determination and courage, you may get frustrated and never continue such a course of study. Mathematics does have a multitude of topics which in return have a host of sub-topics which have many phases and steps to achieving the desired result. In the past, there have been persons who set to complete a course in mathematics but because of the harshness associated with getting it completed, they stop, and some have changed to a different course. In truth and fact, there are some really easy mathematical concepts which take little or no effort to pass through while at the same time, there are some that are not achievable by a long shot. No matter how much work is put into it, it still cannot be accomplished.

For persons who have chosen a course of study in mathematics, they must complete a research paper on a selected topic or on a topic which has been duly assigned to them. From the experience of many students, there have been some topics which have been easy to complete whereas some that have not been accomplished and had to be changed. Due to the complexity of some of the topics, students have voiced their complaints both directly and indirectly about the hardest thesis topics which they have come across. They may seem simple by the mere words, but when the research aspects of it are brought into play, it is stressing and really complicated. These topics have been a part of simple homework and is complicated on its own at that point so with more drastic research and analysis and the need for data-driven results, they have been proven even harder. Among the hardest documented topics are:

  1. Linear algebra – with the many factors and sub-topics associated with this topic, it can certainly be complicated.
  2. Pure geometry – When you think of vectors, line, and data analysis, think complication.
  3. Algebraic Topology -
  4. Real and complex analysis – this is a mixture of testing, research, and deep analysis
  5. Combinatorics
  6. Algebraic geometry
  7. Calculus
  8. Quantum field theory
  9. Linear equations
  10. Numerical Theory
  11. Differential calculus
  12. Integration
  13. Graph theory
  14. Cryptography
  15. Infinity

If these and their respective components aren't the hardest topics students have come across, then all the reviews and interviews have been false. Students have given their perspective on the outcome of their research and presentation of data.

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