CS2800 - Design and Analysis of Algorithms

Meetings  

• Theme 1 : Introduction - 6 meetings

  • Meeting 01 : Thu, Jan 16, 01:00 pm-01:50 pm

  Introduction. Why this course. What is expected from an algorithm. Integer Multiplication Problem.

  References	<a href="./CS2800/introduction.pdf">slides</a> used in the class.
  Exercises
  Reading

  Introduction. Why this course. What is expected from an algorithm. Integer Multiplication Problem.
  

  References

  :

  slides used in the class.

  • Meeting 02 : Mon, Jan 20, 11:00 am-11:50 am

  What does algorithm design involve? Description, termination, correctness, analysis, optimality. Example which demonstrates - JoSAA and SEAT Algorithmic Problem. Stable Matching Problem. Unstable Pairs. Gale-Shapley Algorithm.

  References	<a href="./CS2800/introduction.pdf">slides</a> used in the class.
  Exercises
  Reading

  What does algorithm design involve? Description, termination, correctness, analysis, optimality. Example which demonstrates - JoSAA and SEAT Algorithmic Problem. Stable Matching Problem. Unstable Pairs. Gale-Shapley Algorithm.
  

  References

  :

  slides used in the class.

  • Meeting 03 : Wed, Jan 22, 09:00 am-09:50 am

  Termination, Correctness for Gale-Shapley Algorithm.

  References	<a href="./CS2800/introduction.pdf">slides</a> used in the class.
  Exercises
  Reading

  Termination, Correctness for Gale-Shapley Algorithm.
  

  References

  :

  slides used in the class.

  • Meeting 04 : Mon, Jan 27, 11:00 am-11:50 am

  Optimality of Gale-Shapley Algorithm. Recap of what a good algorithm will consist of. Overview of the course.

  References	<a href="./CS2800/introduction.pdf">slides</a> used in the class.
  Exercises
  Reading

  Optimality of Gale-Shapley Algorithm. Recap of what a good algorithm will consist of. Overview of the course.
  

  References

  :

  slides used in the class.

  • Meeting 05 : Tue, Jan 28, 10:00 pm-10:50 pm

  Review of asymptotic analysis. Common pitfalls and misunderstandings. Fictitious primality checking algorithm.

  References	<a href="./CS2800/introduction.pdf">slides</a> used in the class.
  Exercises
  Reading

  Review of asymptotic analysis. Common pitfalls and misunderstandings. Fictitious primality checking algorithm.
  

  References

  :

  slides used in the class.

  • Meeting 06 : Wed, Jan 29, 09:00 am-09:50 am

  Number theoretic problems. Primality checking problem and connection to LMC course. Algorithm for primality checking. Termination, Correctness, Runtime analysis, Tightness of Analysis, Lowerbounds? Mention AKS algorithm. Algorithms for Addition. High school algorithm for multiplication.

  References
  Exercises
  Reading	<a href="https://www.cse.iitk.ac.in/users/manindra/algebra/primality_v6.pdf">AKS Algorithm</a>

  Number theoretic problems. Primality checking problem and connection to LMC course. Algorithm for primality checking. Termination, Correctness, Runtime analysis, Tightness of Analysis, Lowerbounds? Mention AKS algorithm. Algorithms for Addition. High school algorithm for multiplication.
  

  References	:	None
  Reading	:	AKS Algorithm

• Theme 2 : Divide and Conquer Technique - 12 meetings

  • Meeting 07 : Mon, Feb 03, 11:00 am-11:50 am

  Interger Multiplication problem. Upper and Lower Bounds. Recursive approach via the Russian Peasant algorithm. The 4-way recursive approach. Unfolding method on the recursion tree. Quadratic bound.

  References	[E] Chapter 1, section 1.9
  Exercises
  Reading

  Interger Multiplication problem. Upper and Lower Bounds. Recursive approach via the Russian Peasant algorithm. The 4-way recursive approach. Unfolding method on the recursion tree. Quadratic bound.
  

  References

  :

  [E] Chapter 1, section 1.9

  • Meeting 08 : Tue, Feb 04, 10:00 pm-10:50 pm

  Analysis of the recurrence relation. Karastuba Method. Solving the recurrence relation. Masters Theorem.

  References	Section 1.9 of [E]. See worked out examples in <a href="https://jeffe.cs.illinois.edu/teaching/algorithms/notes/99-recurrences.pdf">this document</a>.
  Exercises
  Reading

  Analysis of the recurrence relation. Karastuba Method. Solving the recurrence relation. Masters Theorem.
  

  References

  :

  Section 1.9 of [E]. See worked out examples in this document.

  • Meeting 09 : Wed, Feb 05, 09:00 am-09:50 am

  Seven Examples of applying masters theorem. Proof of Masters theorem.

  References	Proof of Masters theorem [CLRS]. More examples in <a href="https://jeffe.cs.illinois.edu/teaching/algorithms/notes/99-recurrences.pdf">this document</a>
  Exercises	Complete the proof of case 3 of masters theorem from CLRS.
  Reading	(Optional reading) <a href="https://www.imsc.res.in/~vikram/DiscreteMaths/2010/MasterThmGen.pdf">A generalization of masters theorem.</a>

  Seven Examples of applying masters theorem. Proof of Masters theorem.
  

  References	:	Proof of Masters theorem [CLRS]. More examples in this document
  Exercises	:	Complete the proof of case 3 of masters theorem from CLRS.
  Reading	:	(Optional reading) A generalization of masters theorem.

  • Meeting 10 : Thu, Feb 06, 01:00 pm-01:50 pm

  Quick sort Algorithm. Median as the pivot. Finding the median. Recursive algorithm. Need of finding the median. Attempt on the median of medians.

  References	Section 1.5, 12.8 of [E]
  Exercises
  Reading

  Quick sort Algorithm. Median as the pivot. Finding the median. Recursive algorithm. Need of finding the median. Attempt on the median of medians.
  

  References

  :

  Section 1.5, 12.8 of [E]

  • Meeting 11 : Mon, Feb 10, 11:00 am-11:50 am

  Finding the k-th smallest element in linear time. Correctness proofs. Detailed Analysis. Why group by 5 and not by 3?

  References	Section 1.8 of [E]
  Exercises
  Reading

  Finding the k-th smallest element in linear time. Correctness proofs. Detailed Analysis. Why group by 5 and not by 3?
  

  References

  :

  Section 1.8 of [E]

  • Meeting 12 : Tue, Feb 11, 10:00 pm-10:50 pm

  Counting the number of inversions. The divide and conquer by strengthening the induction/recursion.

  References	Section 5.3 in [KT]
  Exercises	<ul> <li>Which sorting algorithm uses exactly Inv(sigma) many comparisons?</li> <li>How do we do the ranking comparisons that we started out with for arbitrary two permutations?</li> </ul>
  Reading	(Optional) <a href="https://www.cs.dartmouth.edu/~deepc/LecNotes/cs31/lec5.pdf">Additional Lecture Notes</a><br> Is there a better algorithm for counting the number of inversions? Here is <a href="https://people.csail.mit.edu/mip/papers/invs/paper.pdf">an O(n sqrt(log n)) algorithm</a>.

  Counting the number of inversions. The divide and conquer by strengthening the induction/recursion.
  

  References	:	Section 5.3 in [KT]
  Exercises	:	Which sorting algorithm uses exactly Inv(sigma) many comparisons? How do we do the ranking comparisons that we started out with for arbitrary two permutations?
  Reading	:	(Optional) Additional Lecture Notes Is there a better algorithm for counting the number of inversions? Here is an O(n sqrt(log n)) algorithm.

  • Meeting 13 : Wed, Feb 12, 09:00 am-09:50 am

  Closest Pair Problem. Trivial O(n^2) algorithm for 2D case. The sorting-based algorithm for 1D case. Counter example in the 2D case. Divide and Conquer strategy. Combining the solution. The trivial O(n^2) algorithm. Identifying the vertical band of candidates and why it is useless. Tightetening the argument using observations on the grid. O(n log n) algorithm

  References	Section 5.4 in [KT]
  Exercises	Write down formal proofs of Observation 2 and 3. We formally proved Observation 1 in class.
  Reading	(Optional)<ul> <li>Can we generalize to d dimnesions? <a href="">For constant d, we can still do it in O(n log n) time</a></li> <li>Can we do better than O(n log n) time? Here is one - <A href="https://www.sciencedirect.com/science/article/pii/0020019079900851?via%3Dihub">A faster algorithm that runs in time O(n log log n)</a> </li>

  Closest Pair Problem. Trivial O(n^2) algorithm for 2D case. The sorting-based algorithm for 1D case. Counter example in the 2D case. Divide and Conquer strategy. Combining the solution. The trivial O(n^2) algorithm. Identifying the vertical band of candidates and why it is useless. Tightetening the argument using observations on the grid. O(n log n) algorithm
  

  References	:	Section 5.4 in [KT]
  Exercises	:	Write down formal proofs of Observation 2 and 3. We formally proved Observation 1 in class.
  Reading	:	(Optional) Can we generalize to d dimnesions? For constant d, we can still do it in O(n log n) time Can we do better than O(n log n) time? Here is one - A faster algorithm that runs in time O(n log log n)

  • Meeting 14 : Tue, Feb 18, 10:00 pm-10:50 pm

  Maximum-sum Subarray Problem.

  References	Section 4.1, Page 68 of [CLRS]
  Exercises	Try out the idea discussed in the class (of strengthening the recursion) to improve the running time of divide and conquer algorithm to O(n).
  Reading	<a href="https://personal.utdallas.edu/~daescu/maxsa.pdf">Linear time algorithm</a>.

  Maximum-sum Subarray Problem.
  

  References	:	Section 4.1, Page 68 of [CLRS]
  Exercises	:	Try out the idea discussed in the class (of strengthening the recursion) to improve the running time of divide and conquer algorithm to O(n).
  Reading	:	Linear time algorithm.

  • Meeting 15 : Wed, Feb 19, 09:00 am-09:50 am

  Matrix Addition and Multiplication. Vector addition and point-wise multiplication. Convolution of vectors. Trivial upper bounds and analysis.

  References
  Exercises
  Reading

  Matrix Addition and Multiplication. Vector addition and point-wise multiplication. Convolution of vectors. Trivial upper bounds and analysis.
  

  References

  :

  None

  • Meeting 16 : Thu, Feb 20, 01:00 pm-01:50 pm

  Convolution as a polynomial multiplication in time. Trivial algorithm. Strategy of evaluation, multiplication and interpolation. Linear time algorithms for evaluating a polynomial in one value. Quadratic evaluations. Choice of evaluation points. Scope for divide and conquer.

  References	[CLRS] Section 30.1
  Exercises
  Reading

  Convolution as a polynomial multiplication in time. Trivial algorithm. Strategy of evaluation, multiplication and interpolation. Linear time algorithms for evaluating a polynomial in one value. Quadratic evaluations. Choice of evaluation points. Scope for divide and conquer.
  

  References

  :

  [CLRS] Section 30.1

  • Meeting 17 : Mon, Feb 24, 11:00 am-11:50 am

  Roots of unity. Properties. The fast Fourier Transform Algorithm.

  References	[CLRS] Section 30.2
  Exercises
  Reading

  Roots of unity. Properties. The fast Fourier Transform Algorithm.
  

  References

  :

  [CLRS] Section 30.2

  • Meeting 18 : Mon, Mar 03, 11:00 am-11:50 am

  Implementing the interpolation when evaluations are roots of unity. Inverse Fourier Transform using FFT Algorithm.

  References	[CLRS] Section 30.2
  Exercises
  Reading

  Implementing the interpolation when evaluations are roots of unity. Inverse Fourier Transform using FFT Algorithm.
  

  References

  :

  [CLRS] Section 30.2

• Theme 3 : Decrease and Conquer Technique - 6 meetings

  • Meeting 19 : Tue, Mar 04, 10:00 pm-10:50 pm

  Decrease and Conquer Strategy. The case of insertion sort. Breadth First Search, as a decrease and conquer strategy. BFS tree.

  References	[CLRS] Textbook Section 20.2
  Exercises
  Reading

  Decrease and Conquer Strategy. The case of insertion sort. Breadth First Search, as a decrease and conquer strategy. BFS tree.
  

  References

  :

  [CLRS] Textbook Section 20.2

  • Meeting 20 : Wed, Mar 05, 09:00 am-09:50 am

  Correctness proof for BFS Algorithm. Invariants maintained by the algorithm. Single source shortest path in undirected graphs.

  References	[CLRS] Textbook Section 20.2
  Exercises
  Reading

  Correctness proof for BFS Algorithm. Invariants maintained by the algorithm. Single source shortest path in undirected graphs.
  

  References

  :

  [CLRS] Textbook Section 20.2

  • Meeting 21 : Thu, Mar 06, 01:00 pm-01:50 pm

  (Compensatory lecture on Jan 21st) DFS. Running time Analysis. Properties of DFS algorithm. Paranethesis theorem. Examples.

  References	[CLRS] Textbook Section 20.3
  Exercises
  Reading

  (Compensatory lecture on Jan 21st) DFS. Running time Analysis. Properties of DFS algorithm. Paranethesis theorem. Examples.
  

  References

  :

  [CLRS] Textbook Section 20.3

  • Meeting 22 : Mon, Mar 10, 11:00 am-11:50 am

  Proof of Paranthesis theorem. White-path theorem and the proof. DFS forest. Edge classification into tree edges, back edges, forward edges, cross edges.

  References	[CLRS] Textbook Section 20.3
  Exercises
  Reading

  Proof of Paranthesis theorem. White-path theorem and the proof. DFS forest. Edge classification into tree edges, back edges, forward edges, cross edges.
  

  References

  :

  [CLRS] Textbook Section 20.3

  • Meeting 23 : Tue, Mar 11, 10:00 pm-10:50 pm

  Application #1 of DFS: Acyclicity testing. Proof of correctness using white-path theorem.

  References	[CLRS] Textbook Section 20.4
  Exercises
  Reading

  Application #1 of DFS: Acyclicity testing. Proof of correctness using white-path theorem.
  

  References

  :

  [CLRS] Textbook Section 20.4

  • Meeting 24 : Thu, Mar 13, 01:00 pm-01:50 pm

  Application #2 of DFS: Topological Sort of Directed Acyclic Graphs. Example. Proof of correctness.

  References	[CLRS] Textbook Section 20.4 and 20.5
  Exercises
  Reading

  Application #2 of DFS: Topological Sort of Directed Acyclic Graphs. Example. Proof of correctness.
  

  References

  :

  [CLRS] Textbook Section 20.4 and 20.5

• Theme 4 : Greedy Technique - 6 meetings

  • (Upcoming) Meeting 25 : Mon, Mar 17, 11:00 am-11:50 am

  Topic List for the few lectures<br> Minimal Spanning Tree Problem. The naive algorithm. Does Divide and Conquer work? Cut property. Optimal substructure for MST. Greedy Choice Property. Kruskal's algorithm, correctness, running time. An efficient data structure. Union find. Introduction to Amortization. Union Find Data structure : log*(n) analysis. More examples on Amortized Analysis.

  References
  Exercises
  Reading

  Topic List for the few lectures
  Minimal Spanning Tree Problem. The naive algorithm. Does Divide and Conquer work? Cut property. Optimal substructure for MST. Greedy Choice Property. Kruskal's algorithm, correctness, running time. An efficient data structure. Union find. Introduction to Amortization. Union Find Data structure : log*(n) analysis. More examples on Amortized Analysis.
  

  References

  :

  None

  • (Upcoming) Meeting 26 : Tue, Mar 18, 10:00 pm-10:50 pm

  Prims Algorithm. Correctness and Running time. Motivation for Fibonacci Heaps.

  References
  Exercises
  Reading

  Prims Algorithm. Correctness and Running time. Motivation for Fibonacci Heaps.
  

  References

  :

  None

  • (Upcoming) Meeting 27 : Wed, Mar 19, 09:00 am-09:50 am

  Fibonacci Heaps and operations. Amortized Analysis using charging argument.

  References
  Exercises
  Reading

  Fibonacci Heaps and operations. Amortized Analysis using charging argument.
  

  References

  :

  None

  • (Upcoming) Meeting 28 : Mon, Mar 24, 11:00 am-11:50 am

  Single Source Shortest Path (SSSP). A Prims'-like algorithm for SSSP. Proof of correctness for positive edge weighted graphs.

  References
  Exercises
  Reading

  Single Source Shortest Path (SSSP). A Prims'-like algorithm for SSSP. Proof of correctness for positive edge weighted graphs.
  

  References

  :

  None

  • (Upcoming) Meeting 29 : Tue, Mar 25, 10:00 pm-10:50 pm

  Fractional Knapsack, Greedy Choice.

  References
  Exercises
  Reading

  Fractional Knapsack, Greedy Choice.
  

  References

  :

  None

  • (Upcoming) Meeting 30 : Wed, Mar 26, 09:00 am-09:50 am

  Integral Knapsack and a simple 1/2 approximation using greedy algorithm.

  References
  Exercises
  Reading

  Integral Knapsack and a simple 1/2 approximation using greedy algorithm.
  

  References

  :

  None

• Theme 5 : Dynamic Programming Technique - 5 meetings

  • (Upcoming) Meeting 31 : Mon, Mar 31, 11:00 am-11:50 am

  Dynamic Programming algorithm for integral knapsack. O(nW) pseudopolynomial algorithm.

  References
  Exercises
  Reading

  Dynamic Programming algorithm for integral knapsack. O(nW) pseudopolynomial algorithm.
  

  References

  :

  None

  • (Upcoming) Meeting 32 : Tue, Apr 01, 08:00 am-08:50 am

  (may be) Shortest paths in negative edge weighted graphs. Bellman Ford Algorithm, Proof of correctness, Running time.

  References
  Exercises
  Reading

  (may be) Shortest paths in negative edge weighted graphs. Bellman Ford Algorithm, Proof of correctness, Running time.
  

  References

  :

  None

  • (Upcoming) Meeting 33 : Wed, Apr 02, 09:00 am-09:50 am

  Longest Increasing Subsequence in an array.

  References
  Exercises
  Reading

  Longest Increasing Subsequence in an array.
  

  References

  :

  None

  • (Upcoming) Meeting 34 : Mon, Apr 07, 11:00 am-11:50 am

  Longest Path problem in a DAG and LIS problem and Dynamic Programming Solution.

  References
  Exercises
  Reading

  Longest Path problem in a DAG and LIS problem and Dynamic Programming Solution.
  

  References

  :

  None

  • (Upcoming) Meeting 35 : Tue, Apr 08, 10:00 pm-10:50 pm

  Largest Independent Set Problem and Dynamic Programming Solution.

  References
  Exercises
  Reading

  Largest Independent Set Problem and Dynamic Programming Solution.
  

  References

  :

  None

• Theme 6 : Transform and Conquer Technique - 5 meetings

  • (Upcoming) Meeting 36 : Wed, Apr 09, 09:00 am-09:50 am

  Transformation by instance simplifcation or preprocessing: presorting.

  References
  Exercises
  Reading

  Transformation by instance simplifcation or preprocessing: presorting.
  

  References

  :

  None

  • (Upcoming) Meeting 37 : Mon, Apr 14, 11:00 am-11:50 am

  Transformation by Instance Simplification 2: Gaussian Elimination.

  References
  Exercises
  Reading

  Transformation by Instance Simplification 2: Gaussian Elimination.
  

  References

  :

  None

  • (Upcoming) Meeting 38 : Tue, Apr 15, 10:00 pm-10:50 pm

  Transform by preprocessing : input enhancement. Boyer-Moore Algorithm (simplified version).

  References
  Exercises
  Reading

  Transform by preprocessing : input enhancement. Boyer-Moore Algorithm (simplified version).
  

  References

  :

  None

  • (Upcoming) Meeting 39 : Wed, Apr 16, 09:00 am-09:50 am

  Reduction to the same problem but smaller size. We have been doing it already. Divide and conquer or decrease and conquer are examples of such "self-reductions". Transformation by reduction to another problem: we have been doing it already. Multiplication vs Squaring, Computing LCM.

  References
  Exercises
  Reading

  Reduction to the same problem but smaller size. We have been doing it already. Divide and conquer or decrease and conquer are examples of such "self-reductions". Transformation by reduction to another problem: we have been doing it already. Multiplication vs Squaring, Computing LCM.
  

  References

  :

  None

  • (Upcoming) Meeting 40 : Mon, Apr 21, 11:00 am-11:50 am

  buffer

  References
  Exercises
  Reading

  buffer
  

  References

  :

  None

• Theme 7 : Intractability - 5 meetings

  • (Upcoming) Meeting 41 : Tue, Apr 22, 10:00 pm-10:50 pm

  The problem arena. Several problems for which we do not know good algorithms. Some problems have peculiarities. Short easily verifiable sound certificates for membership. The class NP.

  References
  Exercises
  Reading

  The problem arena. Several problems for which we do not know good algorithms. Some problems have peculiarities. Short easily verifiable sound certificates for membership. The class NP.
  

  References

  :

  None

  • (Upcoming) Meeting 42 : Wed, Apr 23, 09:00 am-09:50 am

  Reductions as a tool to classify the unknown. From Clique to Independent Set. Clique to Vertex Cover.

  References
  Exercises
  Reading

  Reductions as a tool to classify the unknown. From Clique to Independent Set. Clique to Vertex Cover.
  

  References

  :

  None

  • (Upcoming) Meeting 43 : Mon, Apr 28, 11:00 am-11:50 am

  Notion of NP-completeness. The Satisfiability problem is NP-complete (without proof). From 3SAT to Vertex Cover Problem.

  References
  Exercises
  Reading

  Notion of NP-completeness. The Satisfiability problem is NP-complete (without proof). From 3SAT to Vertex Cover Problem.
  

  References

  :

  None

  • (Upcoming) Meeting 44 : Tue, Apr 29, 10:00 pm-10:50 pm

  Coping with NP-completeness. Approximation Algorithms. Parameterized Algorithms.

  References
  Exercises
  Reading

  Coping with NP-completeness. Approximation Algorithms. Parameterized Algorithms.
  

  References

  :

  None

  • (Upcoming) Meeting 45 : Wed, Apr 30, 09:00 am-09:50 am

  Model matters - Randomized Algorithms, Distributed Algorithms.

  References
  Exercises
  Reading

  Model matters - Randomized Algorithms, Distributed Algorithms.
  

  References

  :

  None

• Theme 8 : Tutorials, Eval Meetings - 13 meetings

  • Meeting 46 : Thu, Jan 30, 01:00 pm-01:50 pm

  Tutorial 1 questions released on Moodle. <br> Suggestion : Part A to be attempted in class. Part B is to be attempted at home.

  References
  Exercises
  Reading

  Tutorial 1 questions released on Moodle.
  Suggestion : Part A to be attempted in class. Part B is to be attempted at home.
  

  References

  :

  None

  • Meeting 47 : Thu, Feb 13, 01:00 pm-01:50 pm

  Tutorial 2 (was a takehome tutorial on Feb 6th) <br> Tutorial 3 questions released on Moodle.

  References
  Exercises
  Reading

  Tutorial 2 (was a takehome tutorial on Feb 6th)
  Tutorial 3 questions released on Moodle.
  

  References

  :

  None

  • Meeting 48 : Mon, Feb 17, 11:00 am-11:50 am

  Short Exam 1 (Syllabus : upto and including Feb 13, 2025)

  References
  Exercises
  Reading

  Short Exam 1 (Syllabus : upto and including Feb 13, 2025)
  

  References

  :

  None

  • Meeting 49 : Thu, Feb 27, 01:00 pm-01:50 pm

  Quiz 1

  References
  Exercises
  Reading

  Quiz 1
  

  References

  :

  None

  • Meeting 50 : Thu, Mar 06, 02:00 pm-02:50 pm

  Tutorial 4

  References
  Exercises
  Reading

  Tutorial 4
  

  References

  :

  None

  • Meeting 51 : Wed, Mar 12, 09:00 am-09:50 am

  Short Exam 2

  References
  Exercises
  Reading

  Short Exam 2
  

  References

  :

  None

  • (Upcoming) Meeting 52 : Thu, Mar 20, 01:00 pm-01:50 pm

  Tutorial 5

  References
  Exercises
  Reading

  Tutorial 5
  

  References

  :

  None

  • (Upcoming) Meeting 53 : Thu, Mar 27, 01:00 pm-01:50 pm

  Tutorial 6

  References
  Exercises
  Reading

  Tutorial 6
  

  References

  :

  None

  • (Upcoming) Meeting 54 : Thu, Apr 03, 01:00 pm-01:50 pm

  Tutorial 7 Tutorial 8 (take home Tutorial released on Apr 10th)

  References
  Exercises
  Reading

  Tutorial 7 Tutorial 8 (take home Tutorial released on Apr 10th)
  

  References

  :

  None

  • (Upcoming) Meeting 55 : Thu, Apr 17, 01:00 pm-01:50 pm

  Short Exam 3

  References
  Exercises
  Reading

  Short Exam 3
  

  References

  :

  None

  • (Upcoming) Meeting 56 : Thu, Apr 24, 01:00 pm-01:50 pm

  Tutorial 9

  References
  Exercises
  Reading

  Tutorial 9
  

  References

  :

  None

  • (Upcoming) Meeting 57 : Thu, May 01, 01:00 pm-01:50 pm

  Short Exam 4

  References
  Exercises
  Reading

  Short Exam 4
  

  References

  :

  None

  • (Upcoming) Meeting 58 : Fri, May 09, 09:00 am-12:00 pm

  Endsemester Examination

  References
  Exercises
  Reading

  Endsemester Examination
  

  References

  :

  None

• Theme 9 : Missed Lectures - 3 meetings

  • Meeting 59 : Thu, Jan 23, 01:00 pm-01:50 pm

  To be rescheduled - kept as buffer.

  References
  Exercises
  Reading

  To be rescheduled - kept as buffer.
  

  References

  :

  None

  • Meeting 60 : Tue, Feb 25, 08:00 am-08:50 am

  To be rescheduled - kept as buffer.

  References
  Exercises
  Reading

  To be rescheduled - kept as buffer.
  

  References

  :

  None

  • Meeting 61 : Wed, Feb 26, 09:00 am-09:50 am

  References
  Exercises
  Reading

  
  

  References

  :

  None