The document discusses challenges and proposed solutions to effectively integrating mathematics teaching into computer science undergraduate courses. It outlines challenges such as motivating students, dealing with varying intellectual abilities, assessment, and plagiarism. Solutions proposed include relating concepts to real-world examples, providing supplemental advanced material, giving frequent feedback on assessments, and enforcing strict anti-plagiarism policies. Case studies also demonstrate applying concepts like linear algebra, probability, and numerical computing to machine learning, estimation problems, and root-finding.

1. Ideas on an effective integration of
mathematics teaching into CS
undergraduate courses
Mudassir Shabbir - ITU Lahore.
mudassir@rutgers.edu

2. Outline of the Talk
-Outline of the Talk
-List of the courses
-Challenges and Proposed Solution
-Q&A Session

3. List of the courses?
Cal I& II
Discrete Math
Algorithms
Linear Algebra
Differential Eq.
Probability
Theory of Automata
Numerical Computing
Usual load.

4. List of the courses?
Cal I& II
Discrete Math
Algorithms
Linear Algebra
Differential Eq.
Probability
Theory of Automata
Numerical Computing
Problem Solving
Abstract Algebra
Game Theory
Topology
Comp. Geometry
Discrete Optimization
Graph Theory
Extra load.

5. Challenges?

6. Challenges?
Garnering Motivation
Motivation beyond Classroom
Content vs Absorption Capacity?
Dealing with Intelectual Diversity
Assessment and Feedback?
Dealing with Plagiarism

7. Motivation - I
Direct & Indirect Material Motivations

8. Motivation - I
Direct & Indirect Material Motivations
Help finding a job

9. Motivation - I
Direct & Indirect Material Motivations
Help finding a job
Securing admission to MS/PhD

10. Motivation - I
Direct & Indirect Material Motivations
Help finding a job
Securing admission to MS/PhD
Help with Online Work

11. Motivation - I
Direct & Indirect Material Motivations
Help finding a job
Securing admission to MS/PhD
Help with Online Work
Pre-req for other important courses

12. Motivation - I
Direct & Indirect Material Motivations
Help finding a job
Securing admission to MS/PhD
Help with Online Work
Pre-req for other important courses
Needed for research work or Final Project

13. Motivation - I
Direct & Indirect Material Motivations
Help finding a job
Securing admission to MS/PhD
Help with Online Work
Pre-req for other important courses
Needed for research work or Final Project
The Pleasure of Finding Things Out!!!

14. Case Study: Linear Algebra
How Linear Algebra is used in Machine Learning

15. Case Study: Linear Algebra

16. Case Study: Linear Algebra

17. Case Study: Linear Algebra

18. Case Study: Linear Algebra

19. Case Study: Linear Algebra

20. Case Study: Linear Algebra

21. Case Study: Linear Algebra

22. Case Study: Linear Algebra

23. Case Study: Linear Algebra

24. Case Study: Linear Algebra
How many clubs are possible?

25. Case Study: Linear Algebra
How many clubs are possible?
New Laws!! 1. Club size should be odd.

26. Case Study: Linear Algebra
How many clubs are possible?
New Laws!! 1. Club size should be odd.
2. Common members should be even.

27. Case Study: Linear Algebra
How many clubs are possible?
New Laws!! 1. Club size should be odd.
2. Common members should be even.
How many clubs are possible now?

28. Case Study: Linear Algebra
How many clubs are possible?
New Laws!! 1. Club size should be odd.
2. Common members should be even.
How many clubs are possible now?
Linear Algebra tells us no more than n!

29. Case Study: Probability
Goal: Estimate Number of German Tanks

30. Case Study: Probability
Goal: Estimate Number of German Tanks

31. Case Study: Probability
Goal: Estimate Number of German Tanks

32. Q/A i.e., Discussion Session

33. Case Study: Numerical Computing
Goal: Estimate Root of polynomial
1,24,51,10 in sexagesimal
1.41421296 in decimal
Someone approximated
√
2
In 1800 B.C.!!!

34. Case Study: Numerical Computing
Goal: Estimate Root of polynomial
1,24,51,10 in sexagesimal
1.41421296 in decimal
Someone approximated
√
2

35. Case Study: Numerical Computing
Goal: Estimate Root of polynomial
1,24,51,10 in sexagesimal
1.41421296 in decimal

36. Case Study: Numerical Computing
Goal: Estimate Root of polynomial
1,24,51,10 in sexagesimal

37. Case Study: Numerical Computing
Goal: Estimate Root of polynomial

38. Case Study: Numerical Computing
Goal: Estimate Root of polynomial

39. Case Study: Numerical Computing
Goal: Estimate Root of polynomial
Theorem: If x is an overestimate to
√
S then S/x will be an underestimate!

40. Motivation Summary

41. Motivation Summary
- Almost no one likes

42. Motivation Summary
- Almost no one likes

43. Motivation Summary
- Almost no one likes
- But almost everyone likes puzzles and stories

44. Motivation Summary
- Almost no one likes
- But almost everyone likes puzzles and stories
- And luckily, we have a lot of those in math

45. Motivation Beyond Classroom

46. Motivation Beyond Classroom
- Arrange Interactive Sessions with TAs

47. Motivation Beyond Classroom
- Arrange Interactive Sessions with TAs
- Encourage Collaboration

48. Motivation Beyond Classroom
- Arrange Interactive Sessions with TAs
- Encourage Collaboration
- Relate Content with Everyday Experiences

49. Motivation Beyond Classroom
- Arrange Interactive Sessions with TAs
- Encourage Collaboration
e.g., shortest path algorithms can relate to a path for Uber, talk about Graph Algorithms for Instagram
- Relate Content with Everyday Experiences

50. Motivation Beyond Classroom
- Arrange Interactive Sessions with TAs
- Encourage Collaboration
- Spend Class Time Talking about Activities
e.g., shortest path algorithms can relate to a path for Uber, talk about Graph Algorithms for Instagram
- Relate Content with Everyday Experiences

51. Content vs Absorption Capacity

52. Content vs Absorption Capacity
We have three options:

53. Content vs Absorption Capacity
We have three options:
A. Reduce Content Amount
B. Skim “Mathy” Parts
C. Ignore the Capacity and get on with it

54. Content vs Absorption Capacity
We have three options:
A. Reduce Content Amount
B. Skim “Mathy” Parts
C. Ignore the Capacity and get on with it
Solution = αA + (1 − α)B

55. Content vs Absorption Capacity
We have three options:
A. Reduce Content Amount
B. Skim “Mathy” Parts
C. Ignore the Capacity and get on with it
But always give them a glimpse of the
Solution = αA + (1 − α)B

56. Intellectual Diversity in Class.
- Most of your Content Should Address Most of the Class

57. Intellectual Diversity in Class.
However,
- Most of your Content Should Address Most of the Class
This can be very frustrating for a few...

58. Intellectual Diversity in Class.
However,
- Most of your Content Should Address Most of the Class
This can be very frustrating for a few...

59. Intellectual Diversity in Class.
However,
- Most of your Content Should Address Most of the Class
This can be very frustrating for a few...
So always have something for the adventurous folks.

60. Intellectual Diversity in Class.
However,
- Most of your Content Should Address Most of the Class
This can be very frustrating for a few...
So always have something for the adventurous folks.
For example, A link to an Advanced Topic.

61. Intellectual Diversity in Class.
However,
- Most of your Content Should Address Most of the Class
This can be very frustrating for a few...
So always have something for the adventurous folks.
For example, A link to an Advanced Topic.
References For Research papers.

62. Intellectual Diversity in Class.
However,
- Most of your Content Should Address Most of the Class
This can be very frustrating for a few...
So always have something for the adventurous folks.
For example, A link to an Advanced Topic.
References For Research papers.
A bonus Problem.

63. Assessment Feedback

64. Assessment Feedback
More Exams 3 or 4 maybe?

65. Assessment Feedback
More Exams 3 or 4 maybe?
Ask Relevant Problems that they can connect with.

66. Assessment Feedback
More Exams 3 or 4 maybe?
Ask Relevant Problems that they can connect with.

67. Assessment Feedback
More Exams 3 or 4 maybe?
Ask Relevant Problems that they can connect with.
- Discuss Solutions in Class

68. Assessment Feedback
More Exams 3 or 4 maybe?
Ask Relevant Problems that they can connect with.
- Discuss Solutions in Class
- Make sure they learn from their mistakes!

69. Dealing with Plagiarism

70. Dealing with Plagiarism
- Adhere to a no-tolerance Policy

71. Dealing with Plagiarism
- Adhere to a no-tolerance Policy
- Brief them about Seriousness

72. Dealing with Plagiarism
- Adhere to a no-tolerance Policy
- Brief them about Seriousness
- Catch them early on like in the first semester, and in the first homework

73. Dealing with Plagiarism
- Adhere to a no-tolerance Policy
- Brief them about Seriousness
- Catch them early on like in the first semester, and in the first homework
- Viva After Exam
- Quiz After HWs
Employ Counter-measures