Difference between revisions of "CS 2050"

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{{DISPLAYTITLE:CS 2050 - Introduction to Discrete Mathematics}}
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== Overview ==
  
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[[Category:Courses|^CS^CS]]
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CS 2050 is a 3 credit hour CS class taken by CS majors.
  
   
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'''CS 2050''', formally known as '''Introduction to Discrete Mathematics''', is a 3-credit [[Computer Science]] class taken as a core requirement for Computer Science, Computational Media, and Computer Engineering majors. It provides a basic introduction to pure mathematical concepts useful in Computer Science, basic proof writing techniques, and discrete structures common in Computer Science. It is succeeded by [[MATH 3012]].
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==== Topic List ====
  
   
  ⚫
== Workload ==
  +
Like other core CS and Math classes, CS 2050 primarily consists of homework assignments and a set of exams.
  +
  +
Homework assignments are generally split into two categories: a set of problems through the online textbook (similar to MyMathLab in the MATH core sequence), as well as weekly or bi-weekly problem sets. The online textbook homework generally reinforces basic concepts, while the problem sets tend to be slightly more challenging.
  +
  +
Exams test concepts covered in class through multiple choice, short answer, and proof based questions.
  +
  +
{{Collapsed|
  ⚫
== Topics List ==
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|
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The topics covered in the course are as follows:
 
# Propositions and Propositional Logic
  
# Propositions and Propositional Logic
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## Propositions
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## Operations on Propositions
  +
## Truth Tables
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## Implications
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## DeMorgan's Laws
  +
## Propositional Functions
  +
## Quantifiers
  +
## Arguments
 
# Methods of Proof
  
# Methods of Proof
  +
## Direct Proofs
  +
## Contraposition
  +
## Contradiction
  +
## Construction
  +
## Equivalency Proofs
  +
## Casework
 
# Set Theory
  
# Set Theory
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## Sets
  +
## Subsets
  +
## Venn Diagrams
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## Finite Cardinality
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## Power Sets
  +
## Cartesian Products
  +
## Set Operations
  +
## Functions
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## Types of Functions
  +
## Sequences
 
# Induction and Recursion
  
# Induction and Recursion
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## Weak Induction
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## Strong Induction
  +
## Induction and Recursive Problems
 
# Algorithms and Big-O Analysis
  
# Algorithms and Big-O Analysis
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## Formal Definition of Big-O, Big-Omega, and Big-Theta
  +
## Properties of Big-O
  +
## Basic Algorithm Analysis
 
# Introductory Number Theory
  
# Introductory Number Theory
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## Congruence Classes
  +
## Fast Exponentiation
  +
## GCD and Euclid's Algorithm
  +
## Modular Inverse
  +
## Divisibility
 
# Counting, Permutations, and Combinations
  
# Counting, Permutations, and Combinations
  +
## Rules of Counting
  +
## The Principle of Inclusion-Exclusion
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## The Pigeonhole Principle
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## Permutations
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## Combinations
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## The Binomial Theorem
  +
}}
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== Prerequisite Knowledge ==
  +
  +
=== Programming ===
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Very basic programming exposure is required for this course, as a bit of pseudocode will be written during the algorithms section.
  +
  +
=== Mathematics ===
  +
Only basic algebra is required for this course, no calculus is necessary. However, exposure to linear algebra can be useful, especially during the discussion of injective, surjective, and bijective functions, but this is absolutely not required.
   
  +
== Future Outlook ==
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==== How it fits in the Curriculum ====
  
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CS 2050 is simply a core requirement for Computer Engineers, and no class requires it (other than [[CS 3510]] for CompE students with CS threads). On the other hand, for CS majors, especially for those with either the [[Intelligence]] or [[Theory]] threads, CS 2050 is the start to a major prerequisite chain. CS 2050 acts as a prerequisite for CS majors for [[MATH 3012]], and is one of the prerequisites for [[CS 3510]], both of which are prerequisites for theory classes for both the Intelligence and Theory threads, as well as the Theory Thread's Advanced Math Elective.
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CS 2050 is a required class for all CS, CompE, and CM majors. It is one of the lower-divison requirements for CS and CompE. It is also a prerequisite for Algorithms ([[CS 3510]]) and Applied Combinatorics ([[MATH 3012]]), two core requirements for CS majors.
 
   
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== Current Registration Information ==
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== Registration ==
 
CS 2050 is not a linked course but has an optional [[Recitation]]. You must only register for the lecture section (marked with an A, B, C, etc.). Then you have the option (although its recommended) to register for the recitation section, which is under a different course number: CS 2050R. If you decide to register for recitation, you must register for a recitation section with the same leading letter (e.g. if you register for lecture section CS 2050 A, you must register for recitation section CS 2050R A01, A02, etc.).
  
CS 2050 is not a linked course but has an optional [[Recitation]]. You must only register for the lecture section (marked with an A, B, C, etc.). Then you have the option (although its recommended) to register for the recitation section, which is under a different course number: CS 2050R. If you decide to register for recitation, you must register for a recitation section with the same leading letter (e.g. if you register for lecture section CS 2050 A, you must register for recitation section CS 2050R A01, A02, etc.).
   
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=== Equivalent Courses ===
  
=== Equivalent Courses ===
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[[CS 2051 - Honors Introduction to Discrete Math|CS 2051]] is the equivalent honors section of discrete math. It gives equivalent credit.
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[[CS 2051]] is the equivalent honors section of discrete math. It gives equivalent credit.
   
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If you love math and have an interest in learning discrete math at a higher level, consider taking CS 2051 instead. Note that neither CS 2050 nor CS 2051 expect knowledge of proofs in any form.
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CS 2051 goes over all of the CS 2050 topics at a higher level, and covers more topics as well. Assignments are generally more difficulty. If you love math and have an interest in learning discrete math at a higher level, consider taking CS 2051. Note that neither CS 2050 nor CS 2051 expect knowledge of proofs in any form.
   
  +
CS 2051 is suggested for those considering either the Intelligence or Theory threads. If you are unsure on whether you would like one of those threads, but do love math, consider taking CS 2051.
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=== Majors that Require this Class ===
  
   
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== Resources ==
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* Computer Science (pick between CS 2050 and CS 2051)
  
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* Computer Engineering
  
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* Computational Media
  
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[[Category:Courses|^CS lol^CS]]
  

Latest revision as of 15:14, 12 May 2022


CS 2050, formally known as Introduction to Discrete Mathematics, is a 3-credit Computer Science class taken as a core requirement for Computer Science, Computational Media, and Computer Engineering majors. It provides a basic introduction to pure mathematical concepts useful in Computer Science, basic proof writing techniques, and discrete structures common in Computer Science. It is succeeded by MATH 3012.

Workload[edit | edit source]

Like other core CS and Math classes, CS 2050 primarily consists of homework assignments and a set of exams.

Homework assignments are generally split into two categories: a set of problems through the online textbook (similar to MyMathLab in the MATH core sequence), as well as weekly or bi-weekly problem sets. The online textbook homework generally reinforces basic concepts, while the problem sets tend to be slightly more challenging.

Exams test concepts covered in class through multiple choice, short answer, and proof based questions.


Topics List

The topics covered in the course are as follows:

  1. Propositions and Propositional Logic
    1. Propositions
    2. Operations on Propositions
    3. Truth Tables
    4. Implications
    5. DeMorgan's Laws
    6. Propositional Functions
    7. Quantifiers
    8. Arguments
  2. Methods of Proof
    1. Direct Proofs
    2. Contraposition
    3. Contradiction
    4. Construction
    5. Equivalency Proofs
    6. Casework
  3. Set Theory
    1. Sets
    2. Subsets
    3. Venn Diagrams
    4. Finite Cardinality
    5. Power Sets
    6. Cartesian Products
    7. Set Operations
    8. Functions
    9. Types of Functions
    10. Sequences
  4. Induction and Recursion
    1. Weak Induction
    2. Strong Induction
    3. Induction and Recursive Problems
  5. Algorithms and Big-O Analysis
    1. Formal Definition of Big-O, Big-Omega, and Big-Theta
    2. Properties of Big-O
    3. Basic Algorithm Analysis
  6. Introductory Number Theory
    1. Congruence Classes
    2. Fast Exponentiation
    3. GCD and Euclid's Algorithm
    4. Modular Inverse
    5. Divisibility
  7. Counting, Permutations, and Combinations
    1. Rules of Counting
    2. The Principle of Inclusion-Exclusion
    3. The Pigeonhole Principle
    4. Permutations
    5. Combinations
    6. The Binomial Theorem

Prerequisite Knowledge[edit | edit source]

Programming[edit | edit source]

Very basic programming exposure is required for this course, as a bit of pseudocode will be written during the algorithms section.

Mathematics[edit | edit source]

Only basic algebra is required for this course, no calculus is necessary. However, exposure to linear algebra can be useful, especially during the discussion of injective, surjective, and bijective functions, but this is absolutely not required.

Future Outlook[edit | edit source]

CS 2050 is simply a core requirement for Computer Engineers, and no class requires it (other than CS 3510 for CompE students with CS threads). On the other hand, for CS majors, especially for those with either the Intelligence or Theory threads, CS 2050 is the start to a major prerequisite chain. CS 2050 acts as a prerequisite for CS majors for MATH 3012, and is one of the prerequisites for CS 3510, both of which are prerequisites for theory classes for both the Intelligence and Theory threads, as well as the Theory Thread's Advanced Math Elective.

Registration[edit | edit source]

CS 2050 is not a linked course but has an optional Recitation. You must only register for the lecture section (marked with an A, B, C, etc.). Then you have the option (although its recommended) to register for the recitation section, which is under a different course number: CS 2050R. If you decide to register for recitation, you must register for a recitation section with the same leading letter (e.g. if you register for lecture section CS 2050 A, you must register for recitation section CS 2050R A01, A02, etc.).

Prerequisites[edit | edit source]

None! CS 2050 can be taken as a first year class.

Equivalent Courses[edit | edit source]

CS 2051 is the equivalent honors section of discrete math. It gives equivalent credit.

CS 2051 goes over all of the CS 2050 topics at a higher level, and covers more topics as well. Assignments are generally more difficulty. If you love math and have an interest in learning discrete math at a higher level, consider taking CS 2051. Note that neither CS 2050 nor CS 2051 expect knowledge of proofs in any form.

CS 2051 is suggested for those considering either the Intelligence or Theory threads. If you are unsure on whether you would like one of those threads, but do love math, consider taking CS 2051.

Resources[edit | edit source]

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