Transition to Advanced Mathematics?

In summary: Euclid's Elements is a good place to start, and there are plenty of other books with plenty of other proofs. You might enjoy having a look at some of Underwood Dudley's books; they're both fun and instructive.In summary, a student is attempting a double major in physics and math and wants to double up on math courses for the next 2-3 semesters. They are currently taking Calculus II and are wondering about a course called "Transition to Advanced Mathematics" which is a prerequisite for their math major. The course covers proof methods, set theory, functions and relations, cardinality, basic number theory, and completeness of the real number system. While it may be challenging at first, the course is necessary for
  • #1
yUNeeC
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I am a rising sophomore and am currently registered for Physics I (calc) and Calculus II. However, I am attempting a double major (phys, math), and have started late...so I would like to double up on my maths for the next 2-3 semesters.

I am currently learning Calculus II, so when I take the course it should be a breeze. The only other course that counts towards my math major, that I have met the prerequisites for, is "Transition to Advanced Mathematics." I was wandering, what exactly is this course? The only bit of information I have about it is that it's prerequisite is Calc I.

What gets discussed, and is it an intensive course? I'm trying to pack my schedule with as much as I can possibly take, yet don't want to go overboard.

Thanks.
 
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  • #2
yUNeeC said:
"Transition to Advanced Mathematics." I was wandering, what exactly is this course? The only bit of information I have about it is that it's prerequisite is Calc I.

Doesn't your university have a course catalog either in print or on line where you can look up the course description? We have a course by that name here, but I have no idea how well it would match up with your course. For what it's worth, here's our description for it: "It is designed to prepare a student for advanced math courses and will cover concepts and techniques used in studying logic, proofs, set theory, relations, functions, and cardinality of sets."
 
  • #3
Since it's probably specific to your school, you'd need to look at the course description (which should be available in the "undergraduate catalog"... usually available through the registrar's office).

Once you get a course description up, it will help people answer your question better (if it doesn't just answer this for you on its own). you might also want to talk to students at your school who have taken the course... as well as faculty at your school.

Edit -- oops... jtbell beat me to it! I need to type faster!
 
  • #4
Oh, ha. I was in the course catalogue but didn't scroll all the way down.

Here is the description:

2300. Transition to Advanced Mathematics (3) P: MATH 2171. Proof methods including induction, naïve set
theory, functions and relations, cardinality, basic number theory, completeness of the real number system.

I'm sure many people here know of these things...does this sound like either a time-consuming or a difficult course?
 
  • #5
It sounds like something my undergraduate institution called "Intermediate Analysis." I didn't take it; since I was not a math major (rather a math minor), I skipped it and just went straight for the "advanced" courses: Complex Analysis and Real Analysis (which had the intermediate class as a recommended but not required prerequisite). I heard it was tough for some students, and a "cakewalk" for others.

What you might be able to do... see if you can find a course website for one of the more recent classes at your institution... and check out what text is being used. Get a copy (perhaps from the library?) and look over it. Maybe you can even see some notes if those are posted. And again, I'd recommend directly talking to some students at your institution who have taken the course. That's where I always got my course advice (though I didn't always heed it and tended to overload myself!).
 
  • #6
yUNeeC said:
Oh, ha. I was in the course catalogue but didn't scroll all the way down.

2300. Transition to Advanced Mathematics (3) P: MATH 2171. Proof methods including induction, naïve set
theory, functions and relations, cardinality, basic number theory, completeness of the real number system.

I'm sure many people here know of these things...does this sound like either a time-consuming or a difficult course?

Depends on how much you have written proofs before. Writing mathematical proofs isn't easy, and definitely takes some practice until you get comfortable with it. So you might think the course is a little challenging at the beginning. However, it's a very helpful course if you're going to take upper-division math courses. In fact, taking an upper-division math course without any experience on writing proofs would be VERY challenging and time consuming, so this would be a great course to gain some experience. And the things that are listed on the course description is something all the math majors should know. You know you took pre-calculus before you took calculus, right? This course is probably going to be your pre-math major class before you get to the serious stuff.
 
  • #7
Well, I took Intro to Logic last semester, so I know a lot of the rules. I just haven't had to apply them to math before. Not sure if replacing P's and Q's with numbers would be a huge difference, it might be. But I have no experience with mathematical proofs.
 
  • #8
Logic is basically the foundation of mathematics, so you're in a good shape. You do, however, need to apply that logic so that you can write a mathematical proof. It's a little more than just making truth tables, you know.
 
  • #9
Well, we did that, but with sentences. Truth tables were easy...but then came the "turn this into this" and it got pretty complicated. There were over 20 rules, and then the Reductio Ad Absurdum and...something else. I forget.

I suppose that this course would be manageable, even on a already (pretty) heavy load?
 
  • #10
I'm perhaps going to say something heterodox here, but logic is to proofs as syllables are to language. Yes, you need to understand logic and be comfortable with it to do mathematics, but math is much larger than truth tables and what we think of as the rules of logic.

Remember that proofs are a form of communication among humans, not something you program into a computer. Why not have a look at various proofs and see if you can follow them & get a feel for them?
 

1. What is "Transition to Advanced Mathematics"?

"Transition to Advanced Mathematics" is a course designed to help students make the jump from lower-level math courses to more advanced ones. It covers topics such as logic, proofs, sets, and functions that are crucial for success in higher-level math courses.

2. Who should take this course?

This course is typically taken by students who have completed introductory math courses, such as calculus, and are planning to major in a math-related field. It is also recommended for students who want to improve their critical thinking and problem-solving skills.

3. What are the benefits of taking this course?

This course provides a strong foundation for advanced mathematics courses and helps students develop their proof-writing skills, logical reasoning, and abstract mathematical thinking. These skills are not only important for math-related fields, but also for various other disciplines that require analytical thinking.

4. What topics are covered in "Transition to Advanced Mathematics"?

The topics covered in this course may vary depending on the institution, but some common topics include basic logic, set theory, relations, functions, and proof techniques such as direct proof, proof by contradiction, and mathematical induction.

5. How can I prepare for "Transition to Advanced Mathematics"?

To prepare for this course, it is recommended to review basic algebra, trigonometry, and calculus concepts. Familiarizing yourself with proof-writing techniques and practicing them will also be beneficial. Additionally, developing good study habits and time management skills will help you succeed in this course.

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