StudyPath

MAT 223 Real Analysis I

NCE2 levelSciences18 topics

MAT 223 covers 18 topics. StudyPath paces them into daily study sessions that finish before your exam date, with practice questions and worked answers for each one.

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Course outline

The topics this course covers, in teaching order.

  1. Solve abstract problems through the use of mathematical skills.
  2. Use correctly the methods of proofs in mathematics.
  3. Basic properties of real number system including boundedness and completeness
  4. Concept of neighbourhood
  5. Open and close sets
  6. Basic theorems on open and closed sets
  7. De Morgan laws
  8. Function and functional notation
  9. Rigorous treatment of limits and continuity
  10. L’Hospital’s rule (proof may be required)
  11. Consequences of differentiation
  12. Rolle’s theorem
  13. Mean value theorem and Taylor’s theorem (proof may be required)
  14. Successive differentiation
  15. Leibnitz’s formula for nth derivative (proof not required)
  16. Functions of several variables
  17. Partial differentiation
  18. Lagrange’s multipliers

A sample from this course

One topic, as StudyPath teaches it.

Solve abstract problems through the use of mathematical skills.

This topic tests your ability to translate an abstract mathematical statement into precise symbols, choose a suitable method of proof or calculation, and carry the argument through logically. For the exam, you must master definitions, symbolic reasoning, and problem-solving strategies because many Real Analysis questions are less about routine computation and more about clear mathematical thinking.

What you get for MAT 223

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