Module Specifications..
Current Academic Year 2023  2024
Please note that this information is subject to change.
 
Repeat examination 

Description This module introduces students to the formal and rigorous approach to mathematics which underpins mathematical analysis. The students will develop the skills necessary to make the transition from a formulaic understanding of mathematics to constructing their own formal mathematical arguments, and to promote advanced mathematical thinking through the use of guided inquiry and example generation.  
Learning Outcomes 1. interpret the formal mathematical definitions and statements which arise in analysis. 2. classify and describe the main components of the definitions or statements, and the motivation behind them. 3. give examples or counterexamples of important phenomena which are studied in mathematical analysis. 4. critique and explain the logical steps which are required to apply definitions or theorems to the phenomena which occur in mathematical analysis. 5. critique and explain the main logical arguments which occur in the proofs of a selection of theorems. 6. calculate important quantities which arise in mathematical analysis e.g. bounds of sets or sequences, convergence of sequences or series.  
All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml 

Indicative Content and Learning Activities
Real numbers Axiomatic definition of the reals, Inequalities, modulus function, triangle inequality, bounded sets, supremum and infimum Sequences bounded sequences, monotone sequences, convergent sequences, Cauchy sequences, Convergence theorems Applications of sequences Newton approximation for square roots, Exponential function and the logarithm, (Iterated fractions) Application to Differential Calculus Formulation of sequential continuity, Derivative, and Riemann integral in terms of sequences Series Geometric series, Telescoping series, Harmonic series, Leibnitz criterion, absolute convergence, Cauchy product, ratio test, root test Power series Convergence radius, Exponential function, Trigonometric functions, Differentiability, Integrability  
 
Indicative Reading List
 
Other Resources None  
Programme or List of Programmes
 
Archives: 
