What Branch of Math Should I Study?
Choosing the right branch of mathematics to study can be a challenging decision. The vast and diverse landscape of mathematics offers numerous options, and finding the one that truly compels you requires deep introspection and dedication. In this article, we'll explore two key questions to help you make an informed decision. By understanding what compels you and how you plan to apply your knowledge, you can choose a path that aligns with your goals and passions.
Understanding Your Compelling Interests
First, it is crucial to identify what branch of mathematics compels you the most. Passion is a powerful motivator, and in the field of mathematics, a burning desire can make all the difference. Mathematics is a highly abstract discipline that demands extensive mental engagement both during focused work sessions and in quieter moments like when you're in bed or traveling.
Abstract thinking is a core aspect of mathematics, and it involves using your entire brain to make connections and solve complex problems. This mental engagement does not just happen when you're at your desk—it also occurs during rest and during the subconscious processes that occur in your brain while you're not actively engaged in problem-solving.
Consider what areas of mathematics pique your interest. Do you find enjoyment in solving complex proofs? Are you fascinated by the intricacies of numbers and patterns?
Try forcing yourself to study and practice a field for several months without any other distraction. This intense period of focus can help you determine whether a particular branch truly compels you.
Abstraction in mathematics is a mental process that can invigorate you both in challenging times and in moments of repose. Choose a field that aligns with your deepest intellectual interests.
Considering Your Career Goals
The second question to ask yourself is how you plan to make a living from your mathematical knowledge. Your career choice can significantly influence the branches of mathematics you should specialize in. Here are some examples of mathematics-related professions and the fields they are associated with:
Jobs Associated with Various Fields of Mathematics
NSA: Cryptology
Aeronautics: PDFs (Probability Density Functions) and Dynamical Systems
Actuary: Probability and Statistics
Computational Engineering: Numerical Analysis, Graph Theory
Quantum Computing: Functional Analysis
Mathematical Finance: Probability Theory, Stochastics, SPDFs (Stochastic Partial Differential Equations)
Meteorology: Dynamical Systems
Molecular Chemistry: PDFs, Probability Theory
Once you have a list of the fields that interest you, research the associated jobs to further refine your decision. Understanding the job expectations is crucial. Even if you are paid a high salary in a field you adore, if the other aspects of the job make you unhappy, your overall satisfaction will likely be low.
Best Fields to Start with
Based on the information provided, if you're looking for a field that offers the best chance of working in mathematics generally, I would recommend probability and statistics. It is a versatile and widely applicable field with numerous applications across various industries.
Alternatively, if your career goal is in general engineering, you should delve deeply into physics, particularly classical dynamics and thermodynamics, and study the associated mathematics thoroughly. This will provide you with a strong foundation in the mathematical principles underlying these physical phenomena.
Conclusion
Selecting the right branch of mathematics is a personal and highly individual decision. It requires self-reflection, dedication, and a clear understanding of your career goals. By following the steps outlined in this article, you can make an informed choice that aligns with your passions and prepares you for a successful and rewarding career in mathematics or related fields.
Good luck, and may the flame of your passion continue to burn brightly!