Question About a Course on Mathematical Thinking

[sEsposito]

I have to take a required course for my major this fall titled Mathematical Thinking. The course description says something along the ways of "students are expected to give presentations, for examples and counterexamples and proof mathematical theories..." that's not verbatim, but it's what I can remember from the description.

I'm not familiar with this type of class and I'm just wondering if this is a common requirement and what I should expect from this class?

 

[VeeEight]

I am not sure about if this is what you're talking about, but Mathematical Problem Solving is usually offered as a second year undergrad course - see the book the Art of Problem Solving. It is usually along the lines of math competitions (Putnam and all those fun contests) and focuses on develop problem solving skills (proof by contradiction, symmetry, recursion, etc) for various topics rather than developing an entire system of definitions & theorems for only a single topic.

 

[thrill3rnit3]

I have to take a required course for my major this fall titled Mathematical Thinking. The course description says something along the ways of "students are expected to give presentations, for examples and counterexamples and proof mathematical theories..." that's not verbatim, but it's what I can remember from the description.

I'm not familiar with this type of class and I'm just wondering if this is a common requirement and what I should expect from this class?

It's a form of transition from "cookbook style" mathematics (Calculus, LA and DE to a certain extent) to a more "proof-based" mathematics (algebra, analysis, and so on). Some students have trouble making that abrupt switch in mathematical thinking, hence the need for an introductory course to proof. Take the class if you haven't had a good exposure to proofs before.

 

[sEsposito]

It's a form of transition from "cookbook style" mathematics (Calculus, LA and DE to a certain extent) to a more "proof-based" mathematics (algebra, analysis, and so on). Some students have trouble making that abrupt switch in mathematical thinking, hence the need for an introductory course to proof. Take the class if you haven't had a good exposure to proofs before.

Thanks for the explanation, it helped me a lot. It's a required class for me so I have to take it; I'm glad now I know what I'm going into. Thanks again.

 

[rezeew]

I have a strong background in mathematical thinking and can offer some insight into what you can expect from this course. First and foremost, it is common for many majors to require a course in mathematical thinking, as it is a fundamental skill in many fields of study. This course will likely focus on developing your critical thinking and problem-solving skills through the use of mathematical theories, examples, and counterexamples.

In terms of the specific requirements mentioned in the course description, giving presentations and providing examples and counterexamples are important skills in the field of mathematics. Presentations will allow you to communicate your ideas and findings effectively, while examples and counterexamples will help you to understand and apply mathematical theories in a practical way.

Additionally, the emphasis on proof in this course is a crucial aspect of mathematical thinking. Proofs are used to validate mathematical theories and demonstrate their accuracy, and learning how to construct and analyze proofs is a key skill for any mathematician or scientist.

Overall, this course will likely challenge you to think critically and creatively about mathematical concepts, and will provide you with valuable skills that can be applied in various fields. I encourage you to approach this course with an open mind and a willingness to learn, and I am confident that it will be a rewarding experience for you.