1 
Lecture
1: Recalled basics on modular arithmetic and then explained how arithmetic modulo 2 is related to logic. Explained the logical connectibe "AND". 
2 
Lecture
2: Introduced the logical connectives AND and NOT. Explained how to calculate a truth table for a complicated logical expression constructed using AND, OR and NOT. 
3 
Lecture
3 (Guest Lecturer): Introduced the logical connective "implies". 
4

Lecture
4 (Guest Lecturer): Introduced the notion of a tautology and the notion of a contractiction. 
5

Lecture
5: Explained what is meant by a "logically valid argument" and investigated some examples. 
6

Lecture
6: Investigated the logical validity of several arguments. 
7

Lecture
7: Introduced complex numbers and explained how they are added, subtracted and multiplied. 
8

Lecture
8: Explained how to divide one complex number by another. Then introduced the modulus of a complex number and the argument of a complex number. STUDENT ATTENDANCE WAS RECORDED. 
9

Lecture
9: Proved that wz=wz and Arg(wz)=Arg(w)+Arg(z). Then used this result to make some calculations. 
10

Lecture
10 : Explained De Moivre's Theorem and used it to make some calculations. Explained how to factorize the polynomials x^{4}1 and x^{5}1. 
11

Lecture
11: Introduced the notation e^{ix}=cos x + i sin x . Then factorized the polynomial x^{5}1 as a product of real linear and quadratic polynomials. The same method will work for factorizing the polynomials x^{6}1, x^{7}1, ... . 
12

Lecture
12: Solved a complex numbers exam question from the 200607 MA123 exam paper. (This year's MA133/MA135 module is following essentially the same syllabus as the former MA121 & MA123 modules. In the old days there were two 3hour papers in summer, one devoted to calculus and one devoted to algebra, and no Christmas exams. These days we hold a 2hour calculus & algebra exam at Christmas and a 2hour calculus & algebra exam in summer.) 
13

Lecture
13: Solved a system of linear equations using Gaussian elimination. 
14

Lecture
14: Explained how we can regard a linear equation as a plane, and how we can regard the solutions to a system of linear equations as being those points in the intersection of a system of planes. 
15

Lecture
15: Explained that a system of linear equations may have no solution, or it may have just one solution, or it may have infinitely many solutions lying on a line, or it may have infinitely many solutions lying on a plane, or ... . Solved some systems of linear equations. 
16

Lecture
16: Solved some systems of linear equations. 
17

Lecture
17: Explained how matrix notation, and the inverse of a matrix, can be used to solve a system of n equations in n unkowns. 
18

Lecture
18: Explained the GaussJordan (or row operation) method for finding the inverse of a square matrix. 
19

Lecture
19: Revised Logic using problems from the problem sheet. 
20

Lecture
20: Revised problems on complex numbers. 
21

Lecture
21: Revised more problems on complex numbers. Student attendance was recorded. 
22

Lecture
22: 
23

Lecture
23: 
24

Lecture
24: 
1 
Lecture
1: Recalled basic formulae for areas; explained how limits are needed to derive a formula for the area of a circle; introduced the notion of a definite integral. 
2 
Lecture
2: Calculated definite integrals for the functions y=mx+c, y=x+c and y=x^{2}. 
3 
Lecture
3 (Guest Lecturer): Introduced the floor function. Eplained how to calculate the integral of a sum and of a scalar multiple. 
4

Lecture
4 (Guest Lecturer): Introduced the notion of an antiderivative. Stated the Fundamental Theorem of Calculus and used it to compute the integral of a product. 
5

Lecture
5: Recalled the Fundamental Theorem of Calculus, and then gave a proof of it. 
6

Lecture
6: Used integration to solve a range of word problems. 
7

Lecture
7: Solved an integration problem involving acceleration (= rate of change of velocity). Then started to talk about techniques of integration. Covered Technique 1: algebraic simplification. 
8

Lecture
8: More on techniques of integration. Covered Technique 2: spotting integrals of some standard functions. Started Technique 3: simple substitutions. 
9

Lecture
9: More on techniques of integration. Covered Technique 3: simple substitutions. 
10

Lecture
10
: More techniques of integration. Covered integration by parts (ie integration of a product). STUDENT ATTENDANCE WAS RECORDED. 
11

Lecture
11: More techniques of integration: Covered trigonometric substitutions. 
12

Lecture
12: Started to cover the final technique of integration: partial fractions. 
13

Lecture
13: Gave more details and examples on partial fractions. 
14

Lecture
14: Introduced the notion of a differential equation and its solution. Found all solutions of the differential equation dy/dx = ky . Then investigated a cooling cup of coffee. 
15

Lecture
15: Finished the investigation of a cooling cup of coffee. Then explained the Malthusian model of population growth and used it to model the World's population. 
16

Lecture
16: Introduced the Logistic Model of population growth. The Logistic Model is a separable differential equation  so we covered the technique for solving a separable differential equation. 
17

Lecture
17: Solved the Logistic Model and predicted the limiting world population. 
18

Lecture
18: Revised problems on integration from Section 10.7 in the problem sheet. 
19

Lecture
19: Revised more problems on integration. 
20

Lecture
20: Revised problems from Section 10.9 on differential equations. 
21

Lecture
21: Revised more problems on differential equations. 
22

Lecture
22: Revised problems on techniques of integration. 
23

Lecture
23: Revised more problems on techniques of integration. (Recorded attendance.) 
24

Lecture
24: Revised more problems on techniques of integration. (Recorded attendance.) 