Two questions about general math

In summary, the conversation discusses whether a good understanding of proof-based math courses, such as Real Analysis, makes courses based on computations, like Calculus, relatively easy. It is mentioned that in the usual sequence of courses in the US, Calculus is taken before Real Analysis. However, it is argued that knowing Real Analysis is not necessary for solving Calculus problems, but it can be helpful in formulating more advanced problems. The conversation also emphasizes the importance of understanding the subject beyond just solving problems.
  • #1
flamengo
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Is it true that if you have a good understanding of proof based math courses( like Real Analysis), courses based in computations( like Calculus) become relatively trivial ? And I have another doubt. Do I need to know Real Analysis to formulate Calculus problems and exercises ? Or, is a rigorous Calculus book enough for this finality ?
 
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  • #2
The usual sequence of courses in the US are Calculus 1,2,3 and then a year later Real Analysis so that says that solving Calculus problems doesn't require RA.
 
  • #3
My question is not about solving Calculus problems. It's about formulating(creating) Calculus problems.
 
  • #4
flamengo said:
s it true that if you have a good understanding of proof based math courses( like Real Analysis), courses based in computations( like Calculus) become relatively trivial ?
No. How would you prove that your computations are correct? Good courses about computation are more than cookbook classes.
flamengo said:
Do I need to know Real Analysis to formulate Calculus problems and exercises ? Or, is a rigorous Calculus book enough for this finality ?
No, I don't think so, not for the "drill" exercises in any case. However, the more you are "above" the subject, the better. Also, I could certainly think of more advanced calculus problems that require an understanding of real analysis for their proper design.
 
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Related to Two questions about general math

1. What is the difference between arithmetic and algebra?

Arithmetic is the branch of mathematics that deals with basic operations like addition, subtraction, multiplication, and division. Algebra, on the other hand, involves solving equations and manipulating symbols to find unknown values.

2. How can I improve my mental math skills?

To improve your mental math skills, you can practice doing calculations in your head, use mental math tricks and shortcuts, and regularly review and practice basic math concepts.

3. What are the fundamental principles of geometry?

The fundamental principles of geometry are points, lines, and planes. Points are represented by a dot and have no size or dimension. Lines are made up of infinitely many points and have length but no width. Planes have length and width, but no thickness.

4. How can I solve word problems in math?

To solve word problems in math, you can follow the steps of identifying the known and unknown values, translating the problem into an equation, and solving the equation to find the answer. It is also helpful to draw diagrams or use tables to organize information.

5. What is the order of operations in math?

The order of operations in math is a set of rules that dictate the order in which mathematical operations should be performed. The acronym PEMDAS can be used as a guide, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

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