ND 2 ELECT/ELECT FIRST SEMESTER MTH 212 (MAPOLY)

MTH 212 LOGIC AND LINEAR ALGEBRA COURSE OUTLINE

1.1 The essential connectives, negation, conjunction, disjunction, implication and bi-implication

1.2 State the essential connectives defined in 1.1 above.

1.3 Explain grouping and parenthesis in logic,

1.4 Explain Truth Tables.

1.5 Define tautology

1.6 Give examples of types of tautology. e.g

5. If P and Q are distinct atomic sentences,

which of the following are tautologies?

(a) P - Q (b) PUQ - QUP (c) PV(P*Q)

ii. Let P = Jane Austen was a contemporary

of Beethoven.

Q = Beethoven was a contemporary of

Gauss.

R = Gauss was a contemporary of

Napoleon

S = 'Napoleon was a contemporary of Julius

Caesar'.

(Thus P, Q and R and true, and S is false).

Explain and illustrate 1.1 to 1.6

Then find the truth values of sentences:-

(a) (P *Q) = R

(b) (P - Q)

(c) P *Q - R - S

3 - 4

1.7 Define universal quantifier and existential quantifier.

1.8 Translate sentences into symbolic form using quantifiers. e.g. 'some freshmen are intelligent' can be stated as for some x, x,is a freshman and x is intelligent' can translate

in symbols as (/x) (Fx & Ix).

1.9 Define the scope of a quantifier

1.10 Define 'bound' and 'free' variables

1.11 Define 'term' and formula'

1.12 Give simple examples of each of 1.9 to

1.13 Explain the validity of formulae

2.1 Define permutations and combinations

2.2 Give illustrative examples of each of 2.1 above

2.3 State and approve the fundamental principle of permutation.

2.4 Give illustrative examples of the fundamental principles of permutation.

2.5 Establish the formula nPr= n!/ (n - r)!

2.6 Prove that nPr = (n - r + 1) x nP (r - 1).

2.7 Solve problems of permutations with

restrictions on some of the objects.

2.8 Solve problems of permutations in which

the objects may be repeated.

2.9 Describe circular permutations.

2.10 Solve problems of permutation of N things not all different.

2.11 Establish the formula nCr= n!/[(n - r)! r!]

2.12 Solve example 2.11

2.13 State and prove the theorem nCr= nCn-r

2.14 Solve problems of combinations with restrictions on some of the objects.

2.15 Solve problems of combinations of n different things takenany number at a time.

General Objective 3.0: Know binomial theorem

3.1 Explain with illustrative examples - the method of mathematical induction.

3.2 State and prove binomial theorem for positive integral index.

3.3 Explain the properties of binomial expansion.

3.4 State at least seven (7) examples of 3.3 above. e.g. i. A (x2- 1/x) ii. Find the constant term in the expansion of (x + 1/x)A

iii. Find the co-efficient of xv In the expansion of (x +k)Awhere v is a number lying between -n and n-

3.5 State the binomial theorem for a rational number

3.6 State the properties of binomial co-efficients.

3.7 Apply binomial expansion in approximations (simple examples only).  

4.1 Define Matrix

4.2 Define the special matrices - zero matrix, identify matrix - square matric, triangular matrix, symmetric matrix, skero symmetric matrix.

4.3 State example for each of the matrices in 4-2 above.

4.4 State the laws of addition and multiplication of matrices.

4.5 Illustrate the commutative, associative, and distributive nature of the laws states in

4.6 Explain the transpose of a matrix.

4.7 Determine a determinant for 2by2and 3by2matrices.

4.8 Define the minors and cofactors of a determinant.

4.9 Explain the method of evaluating determinants.

4.10 State and prove the theorem "Two rows or two columns of a matrix are identical, then the value of it's determinant is zero".

4.11 State and prove the theorem "If two rows or two columns of a matrix are  interchanged, the sign of the value of its determinant is changed".

4.12 State and prove the theorem "If any one row or one column of a matrix is multiplied by a constant, the determinant itself is multiplied by the constant".

4.13 State and prove the theorem "If a constant times the elements of a row or a

4.14 State five examples of each of the theorems in 4. 10-4 13 above.

4.15 Define the adjoint of a matrix

4.16 Explain the inverse of a matrix.

4.17 State the linear transformations on the rows and columns of a matrix.

4.18 Apply Crammer's rule in solving simultaneous linear equation.

4.19 Apply Linear transformation in solving simultaneous linear equations.