Introduction to Analysis

From this page you can access a collection of materials dealing with some important areas of introductory Analysis. For Maynooth University students, this material is typically covered in parts of Introduction to Analysis (MT432D) and Analysis 1 (MT432C). These resources are not a replacement for the material covered in your lectures and assignments, rather you should use them as extra support to aid your understanding of any material you may have difficulties with.

• Videos on Basic Set Operations - Union, Intersection, Complements, Notation, Universal Set, Subsets, Compositions of Operations (Khan Academy)
• Notes on Sets, Set Notation, Functions, Equivalence Relations, Bijections & Inverse Functions, Cardinality (University of Louisville)
• Notes on Sets & Set Notation (MathCS)
• Notes on Relations & Functions (MathCS)
• Notes on the sets of Natural and Rational numbers, and the set of Integers (MathCS)
• Notes on Countable Infinity (MathCS)
• Notes on Uncountable Infinity (MathCS)
• Notes on Induction (MathCS)
• Videos on Logic, Formal Proofs, Induction, Set Theory & Set Operations, Mappings Basic Properties, Composition & Inverse, Cardinality of Finite & Infinite Sets, Divisibility & Euclidean Algorithm (MathDoctorBob)
• Video on One-to-One & Onto Functions (Khan Academy)
• Videos on Real Analysis - Introduction, Countable Partition, Induction, Cardinality of [0,1], Cauchy Sequences (MathDoctorBob)
• Notes on the Irrationals Pi & e (MathCS)
• Notes on Sequences (MathCS)
• Videos on Limits - Epsilon-Delta Proofs (Khan Academy)
• Video on Limits - Epsilon-Delta Proofs (MathDoctorBob)
• Notes & Questions on Limits - Epsilon-Delta Proofs (UC Davis)
• Notes on Cauchy Sequences (MathCS)
• Notes on Sub-sequences (MathCS)
• Notes on Lim Sup & Lim Inf (MathCS)
• Notes on Series & Convergence (MathCS)
• Notes on Convergence Tests (MathCS)
• Notes on Real Numbers, Sequences & Series, Limits & Continuity (Wikibooks)