Programs Deciding between Applied Math and Math as my second Major?

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A computer science major considering a double major in math is weighing the benefits of applied versus pure mathematics. The individual is currently facing challenges in an Honors Calculus III course, which differs significantly from high school math due to its emphasis on rigorous proofs. Despite the difficulty, there is an enjoyment in the challenge. Relevant pure math topics for computer science include combinatorics, discrete math, logic, set theory, number theory, and linear algebra, which are essential for understanding computer science theory. The relationship between computer science and applied math is seen as focused on creating efficient algorithms for computational tasks. It is suggested that taking an introductory proof course may help in transitioning to more advanced pure math courses, which involve proving mathematical concepts rather than just applying theorems. The distinction between pure and applied math is emphasized, with pure math focusing on theoretical foundations and proofs, while applied math centers on practical computation techniques. Overall, pursuing math alongside computer science is viewed as a beneficial and enlightening endeavor.
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I'm a computer science major. I plan to double in math, but, for a computer science major, would I be better off studying applied math?

Right now, I'm not doing as well in my Honors Calculus III course as I have in earlier math classes. (I have a B.) It isn't like anything I did in high school. I never had to write "rigorous proofs." Even though this course has been difficult for me, I find it extremely enjoyable and challenging.
 
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I'm currently starting compEE engineering and doing something with pure maths.

Some pure maths I've researched to be relevant to computer science topics include combinatorics, discrete maths, math logic and set theory, number theory, and linear algebra. There are likely more too. I would google "computer science and <insert course here>"

If you want to focus on computer science theory, then coursework in those classes listed are very useful.

I currently see the relationship between computer science and applied math as: making efficient programs and algorithms for computers to handle computation of such maths. (if anyone disagrees, help expand my perspective).

These pure courses requires efficiency in proof writing and understanding. You may want to tackle an intro to proof course (discrete math in some schools) before going into them.

Pure math and applied math differ. So far, my applied math courses focused on using theorems to create techniques for computation/solving. These include calculus, differential equations, numerical analysis, etc. Pure maths have been mostly proving consequences among consequences originating from accepted truths that describe a mathematical object. These classes are likely something you have never seen before. Additional pure courses are analysis (proof based calculus), abstract algebra (whatever it is, I'll find out soon) and topology (same).

Math is full of challenge and enlightment. Certainly a great subject to pursue on the side.

Edit: moar english fix
 
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