Real Analysis I,

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Course Code: 
MTH 2101
Course Credit Units: 
3
Semester: 
Semester 1
Year of Study: 
Year 2
Undergraduate or Graduate Level: 
Undergraduate Level
Course Description & Objectives: 

This course consists of understanding and constructing definitions, theorems, propositions, lemmas, etcetera and proofs of fundamental ideas/statements in Calculus. It is considered one of the more demanding undergraduate Mathematics courses, but one that every Mathematician should do. The key words in the course are ‘rigor’ and ‘proof. Course Objectives:This course is intended ; 

  • To impart competence in making rigorous proofs of statements in Mathematics
  • To provide a rigorous development of the fundamental ideas of Calculus
  • To develop the student’s ability to handle abstract ideas of Mathematics and Mathematical proofs

 

Learning Outcomes: 
  • competence in making rigorous proofs of statements in Mathematics
  • ability to prove the limit of a sequence, to determine whether a sequence converges or not, to prove the limit of a function, to determine whether or not a function is continuous
  • ability to use tests of convergence to determine whether or not a series converges, determine whether a power series converges and also determine its radius of convergence
  • provide a rigorous development of the fundamental ideas of Calculus
  • ability to handle abstract ideas of Mathematics and Mathematical proofs

 

Real Analysis I
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