CR: COMP 1805 Learning Objectives

Assumed Background

I am assuming that the students will do this course in 2nd term of their first year. At least one course in Grade 12 Mathematics (with U TAG) Completed MATH 1007 (Elementary Calculus) with a grade of ... Either completed or concurrently registered in MATH 1104 (Linear Algebra)

Should have reasonable idea of

• 1. Given a solution for a Grade 12 Math problem, should be able to verify it with minimal help.
• 2. Should have Mathematical sophistication, for example should be able to solve/show that
  • Sum of two odd numbers is even
  • Not all real numbers are rationals
  • The number of prime numbers is infinite
  • The number of possible subsets of set of size n is 2^n
  • Should know the meaning and significance of basic functions: log x, e^x, x^2, x, x^3
  • Should know what is a function, what are properties of function.
  • Given a system three linear equations, in three variables, should know how to solve it.
  • Should know how to solve a quadratic equation
  • Should know how to compute a formula for the sum of first n natural numbers.

....

Learning Objectives

Objectives for the whole course

• Mathematical Reasoning: Should be able to read, comprehend and construct mathematical arguments. Should develop sufficient background in mathematical logic, and should be able to apply to construct proofs. Learn some of the standard proof techniques (contradiction, induction, ..).
• Combinatorial Analysis: Ability to count and enumerate objects.
• Number Representation: Learn Bits, Bytes, Binary Representation, Floating-point representation, what is a 64-bit machine?
• Discrete Structures: Ability to work with discrete structures - abstract mathematical structures which are used to represent discrete objects and the relationships between objects. Examples of these structures include sets, permutations, relations, graphs, trees, finite-state machines.
• Algorithmic Thinking: Solving problems by a step-by-step process (algorithm), described in a pseudo-code. Students will get some idea on how to specify the algorithm, how to argue about its correctness, and how to argue about the computational resources (time and space) being used. (Simple algorithms like, Euclid GCD, Binary search, Merge-Sort, breadth-first search, MST, etc. can be discussed.)

Topics

This list is mostly with respect to ROSEN's Discrete Math 6th edition:

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Topic 2

Learning objectives for topic 2