University Mathematics Abstraction

In summary, the conversation discusses the speaker's dilemma in choosing a stream for their second year of study as a MathPhys student. They have narrowed down their options to a combination of ACM, pure maths, and stats or ACM, TP, and Physics. The speaker also expresses their struggles with abstraction and their plans to review concepts over the summer. They seek advice and opinions from others who may have had similar experiences with abstraction in university mathematics. The conversation also touches upon the importance of technical writing and developing a good intuition for mathematical topics.
  • #1
I'm currently a first year MathPhys student, and next year I have to decide my stream. I can pick a combination (pure) Mathematics, Applied & Computationtal. Mathematics, Statistics, MathSci, Physics, Theoretical Physics or Physics with Astronomy & Space. Naturally there are restrictions, and I have narrowed it down to

- ACM, pure maths and stats. This will allow me to pursue any of these degrees, a joint honours between two of the subjects or MathSci.
- ACM, TP and Physics. This will allow me to pursue one of the degrees.I found the physics modules very bland and unsubstantial this year, so am leaning towards picking the first choice. I am however struggling currently with abstraction. It was introduced at the end of Linear Algebra in the context of vector spaces etc. and currently I am taking Real Analysis which I find very challenging. I am worried if I proceed into a mathematics course the level of abstraction and my ability to deal with it will become overwhelming and I simply will not be able to cope. Despite it being challenging, I find aspects of analysis interesting, such as Cardinality for example.

I think because I have never had to think in such a manner, there were no introduction abstraction or set courses and me not working hard enough this year has led me to this fear. Even if I had worked harder I still do not know if this would have allowed me to cross the conceptual gap over to the world of abstraction. I plan to spend some of the summer reviewing various aspects of analysis and abstract algebra with the aim of qeulling my fears, however I have to decide my subjects by July, so I am limited with time.

Has anyone on the forums ever had similar experiences with abstraction or more so University Mathematics in general? Any advice, suggestion or opinion would be most welcome; I am apprehensive to find some sort of potential solution to this problem.
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  • #2
KevinM said:
Has anyone on the forums ever had similar experiences with abstraction or more so University Mathematics in general? Any advice, suggestion or opinion would be most welcome; I am apprehensive to find some sort of potential solution to this problem.

One way to evaluate your talent for abstract mathematics is to observe how you do technical writing and speaking about non-mathematical subjects - something as simple (or complicated!) as directions for changing the oil in car. Do you write precisely? Can you take a legalistic and hair splitting approach to things ? Formulating thoughts in higher mathematics is done in English (or in whatever your native "common language" is). Some people never master technical writing. They expect to express mathematics in a sequence of "steps" that solve a problem.

At the undergraduate level, most people begin by having or developing a good intuition about a mathematical topic (e.g. vectors). Then they superimpose a precise technical view of the subject over that intuition. So there is also the question of whether you can develop a good intuition for mathematical topics. I think that must be considered on a topic-by-topic basis.

What is "University Mathematics Abstraction"?

"University Mathematics Abstraction" is a course or field of study within mathematics that focuses on abstract mathematical concepts and theories, rather than concrete applications or calculations. It is often taken by students who have a strong understanding and interest in mathematics and wish to pursue higher level mathematics courses.

Why is it important to study "University Mathematics Abstraction"?

Studying "University Mathematics Abstraction" allows students to develop critical thinking and problem-solving skills. It also provides a foundation for more advanced mathematics courses, as abstract concepts are often used in higher level mathematics. Additionally, many fields, such as physics and computer science, rely heavily on abstract mathematics, making it a valuable skill for a variety of careers.

What topics are typically covered in "University Mathematics Abstraction"?

Topics covered in "University Mathematics Abstraction" may include set theory, logic, abstract algebra, topology, and analysis. These topics involve understanding and manipulating abstract mathematical structures, such as groups, rings, and metric spaces.

What are some challenges students may face in "University Mathematics Abstraction"?

One of the main challenges in "University Mathematics Abstraction" is the shift from concrete, computational mathematics to abstract, theoretical mathematics. This can be difficult for students who are used to solving problems by following a specific algorithm. Additionally, the concepts and theories covered may be more complex and require a deeper understanding of mathematical principles.

What resources are available for students learning "University Mathematics Abstraction"?

There are many resources available for students learning "University Mathematics Abstraction". These may include textbooks, online lectures and tutorials, practice problems, and study groups. Additionally, professors and teaching assistants are often available for one-on-one help and clarification of difficult concepts.

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