Real Analysis: MAT 303, Supplementary Examinations November 2024
| dc.contributor.author | Ngcibi, S. | |
| dc.contributor.author | Nkonkobe, S. | |
| dc.date.accessioned | 2025-07-01T08:52:14Z | |
| dc.date.available | 2025-07-01T08:52:14Z | |
| dc.date.issued | 2024-11 | |
| dc.description | Real Analysis: MAT 303, Supplementary Examinations November 2024 | |
| dc.description.abstract | This abstract summarizes the MAT 303 Supplementary Examination in Real Analysis, held in January 2024 at the University of Fort Hare. The exam is 3 hours long and carries a total of 100 marks. Dr. S. Ngcibi is the Internal Examiner, and Dr. S. Nkonkobe is the External Examiner. Candidates are instructed to answer all questions, and all symbols used retain their usual meaning. The examination covers fundamental concepts in Real Analysis, structured into three main questions: Question 1 focuses on set theory and topology, including definitions of countable and compact sets, the Cantor-Schröder-Bernstein Theorem, proofs related to injective and bijective functions, properties of open sets, and the Monotone Convergence Theorem for sequences. Question 2 delves into limits and continuity of functions. It requires stating and proving the Bolzano-Weierstrass Theorem for sequences, defining the limit of a function, proving limits using the definition, and defining and demonstrating uniform continuity. Question 3 addresses Riemann Integration. Topics include defining upper and lower sums of a function relative to a partition, defining a refinement of a partition, proving relationships between lower sums and refined partitions, defining upper and lower integrals, and proving properties of integrable functions, specifically the additivity of integrals. | |
| dc.identifier.uri | http://hdl.handle.net/20.500.11837/2936 | |
| dc.language.iso | en_US | |
| dc.publisher | University of Fort Hare | |
| dc.title | Real Analysis: MAT 303, Supplementary Examinations November 2024 | |
| dc.type | Learning Object |