This course covers the mathematical foundations of computer science and engineering.
It introduces elementary concepts in mathematics such as definitions, logic, proofs, functions, relations and counting principles.
The course also introduces students to elementary discrete structures such as sets, partial orders, graphs and trees.
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Objectives
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1.Logic
a. Propositional logic
b. Truth tables
c. Propositional Equivalence
d. Implication, equivalence, converse, inverse, contrapositive and negation
e. Predicates and quantifier
f. Rules of inference
2.Sets
a.Venn diagrams
b.Sets operations
c.Cartesian product
d.Power sets
e.Cardinality of finite sets
f.Important numeric sets, notation and subset relations among them
3.Basic modular arithmetic
a.Division and the division algorithm
b.Congruence, properties and modular arithmetic
c.Application of congruence
4.Functions
a.Representation
b.Surjections, injections and bijections
c.Inverse
d.Composition
e.Important Numeric functions: floor, ceiling, log
5.Proofs
a. Direct proofs
b. Proof by contradiction
c. Proof by contrapositive
6.Sequence and Sums (Basics, more in probability course)
a.Arithmetic and geometric sequences
b.Basic summation techniques and their visualization
c.Linearity of summation
d.Sums of powers of integers
7.Induction
a.Mathematical Induction
b.Weak and strong induction
c. Recursive definitions of functions and sequences
d. Recurrence relation
8.Relations
a. Reflexivity, symmetry, transitivity
b.Operations, union, intersection, complement, projection, join
c. Composition and exponentiation
d. Equivalence relations and equivalence classes
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Description
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