# Course 2BA1 - Mathematics

## Lecture Notes for the Academic Year 2008-09

The course includes the following sections (together with other material not yet available in final form online):-

• Section 1: The Principle of Mathematical Induction [PDF]
• Section 2: Sets and functions [PDF]
• Section 3: Graph Theory [PDF]
• Section 4: Abstract Algebra [PDF]
• Section 5: Formal Languages [PDF]
• Section 6: Vectors [PDF]
• Section 7: Quaternions and Rotations [PDF]
• Section 8: Introduction to Number Theory and Cryptography [PDF]
• Section 9: Differential Equations [PDF]
• Section 10: Trigonometric Identities, Complex Exponentials and Periodic Sequences [PDF]
• Section 11: Periodic Functions and Fourier Series [PDF]

## Assignments in the Academic Year 2008-09

Students are required to complete the following assignments:---

• Assignment 1 [PDF]
• Assignment 2 [PDF]
• Assignment 3 [PDF]

## Other Material for the Academic Year 2008-09

• Worked Solution to Problems concerning Differential Equations and Fourier Series [PDF]
• Supplement concerning Integration by Parts [PDF]

## Lecture Notes for the Academic Year 2007-08

Lecture notes are available for the first semester of 2BA1 in 2007-08 here (in PDF format)

## Assignments in the Academic Year 2007-08

Students are required to complete the following assignments in the first semester:-

• Assignment 1 [PDF]
• Assignment 2 [PDF]
• Assignment 3 [PDF]

## Sample Problems in the Academic Year 2007-08

• Sample problems concerning mathematical induction [PDF]
• Sample problems concerning sets and functions [PDF]
• Sample problems concerning formal languages [PDF]
• ## Lecture Notes for the Academic Year 2006-07

The course consists of the following sections:-

• Section 1: The Principle of Mathematical Induction [PDF]
• Section 2: Trigonometric and exponential functions [PDF]
• Section 3: Differential equations [PDF]
• Section 4: Introduction to Fourier methods [PDF]
• Section 5: Sets and functions [PDF]
• Section 6: Vectors [PDF]
• Section 7: Abstract algebra [PDF]
• Section 8: Quaternions and rotations [PDF]
• Section 9: Introduction to number theory and cryptography [PDF]
• Section 10: Graph theory [PDF]
• Section 11: Formal languages [PDF]

## Lecture Notes for the Academic Year 2005-06

The course consisted of the following sections:-

• Section 1: The Principle of Mathematical Induction [PDF]
• Section 2: Sets and Functions [PDF]
• Section 3: Graph Theory [PDF]
• Section 4: Vectors [PDF]
• Section 5: Abstract Algebra [PDF]
• Section 6: Formal Languages [PDF]
• Section 7: Trigonometric and Exponential Functions [PDF]
• Section 8: Differential Equations [PDF]
• Section 9: Introduction to Number Theory and Cryptography [PDF]
• Section 10: Introduction to Fourier Methods [PDF]

## Assignments in the Academic Year 2006-07

Students were required to complete the following assignments:-

• Assignment 1 [PDF]
• Assignment 2 [PDF]
• Assignment 3 [PDF]

## Assignments in the Academic Year 2005-06

Students were required to complete the following assignments:-

• Assignment 1 [PDF]
• Assignment 2 [PDF]
• Assignment 3 [PDF]

## Assignments in the Academic Year 2004-05

In the academic year 2004-05 students were required to complete the following assignments:-

• Assignment 1 [PDF]
• Assignment 2 [PDF]
• Assignment 3 [PDF]
• Assignment 4 [PDF]

## Assignments in the Academic Year 2003-04

• Assignment 1 [PDF]
• Assignment 2 [PDF]
• Assignment 3 [PDF]
• Assignment 4 [PDF]

## Assignments in the Academic Year 2002-03

• Assignment 1 [PDF]
• Assignment 2 [PDF]
• Assignment 3 [PDF]
• Assignment 4 [PDF]
• Assignment 5 [PDF]

## Assignments in the Academic Year 2001-02

• Assignment 1 [PDF]
• Assignment 2 [PDF]
• Assignment 3 [PDF]
• Assignment 4 [PDF]
• Assignment 5 [PDF]
• Assignment 6 [PDF]

## Assignments in the Academic Year 2000-01

• Assignment 1 [PDF]
• Assignment 2 [PDF]
• Assignment 3 [PDF]
• Assignment 4 [PDF]
• Assignment 5 [PDF]

## The Seven Bridges of Königsberg

Dr. David R. Wilkins
School of Mathematics, Trinity College, Dublin 2, Ireland
dwilkins@maths.tcd.ie