1.1. Goodbye and Farewell

Hello everyone, so this is the farewell lecture with I have already concluded the course, whatever I have promised at the beginning of the course, I have covered hopefully. So, let me again quickly go through what we have learnt in this course.

In this part of the lecture, the professor is addressing the students with a goodbye message. He reflects on the course's journey and acknowledges that he has covered all the topics he promised at the beginning. Essentially, he is wrapping up the course by preparing to summarize key learnings.

Think of this as the final chapter of a book where the author summarizes all the key points discussed in the earlier chapters before concluding the story.

The main objective of the course was to think logically and mathematically and we have covered various topics in this course, starting with mathematical reasoning, where we have seen how to write various types of proofs, understand the proof and so on.

Here, the professor emphasizes the primary aim of the course: to enhance logical and mathematical thinking. He mentions that they kicked off the course by exploring mathematical reasoning, which included learning how to formulate and understand different proofs. This foundational skill is crucial in mathematics and computer science.

Imagine learning to cook; the first step is to understand the basic techniques and recipes. Similarly, in this course, students started by mastering proofs, which are essential 'recipes' for solving problems in mathematics.

We have done lots of combinatorial analysis, we have seen various advanced counting mechanisms like counting by formulating recurrence equations and solving them. We have seen various discrete structures like sets, relations and we have also touched upon basic concepts from graph theory.

In this segment, the professor discusses specific topics covered in the course, particularly combinatorial analysis and discrete structures. He mentions advanced counting techniques, which enable students to solve complex problems systematically. Additionally, he notes the introduction of basic concepts from graph theory, which further illustrates the relationships between different entities.

Think of combinatorial analysis as organizing a party. You need to count how many different ways you can arrange tables, seating, and food. Discrete structures, like graphs, help visualize connections among guests, making planning simpler.

And as I said at the beginning of this course that the concepts that we learned in this course, they are very useful in any area of computer science like algorithms, machine learning, artificial intelligence, cryptography etc.

Here, the professor reiterates the practical importance of the concepts learned in the course and their applicability across various fields in computer science such as algorithms, machine learning, and cryptography. This highlights that the skills and knowledge gained are not just theoretical but have real-world significance.

Consider the tools in a toolbox; each tool has its specific use. The concepts learned in this course are like specialized tools for tackling various problems in the vast landscape of computer science.

I would like to dedicate this course to my beloved gurus of IIT Madras who built my foundations in theoretical computer science, namely Professor Kamala Krithivasan, Professor C. Pandu Rangan and Professor S.A. Choudum.

In this part, the professor expresses gratitude to his mentors who played a significant role in shaping his understanding of theoretical computer science. Acknowledging mentors fosters a sense of community and respect in academia.

Just like a student who credits their teachers for their success, the professor honors his own educators for laying the groundwork for his knowledge and expertise.

And some advertisements from my side, so apart from the course on discrete maths, I also offer a course on foundations of cryptography. So, you can find the details here and it covers in detail all the foundations for modern cryptography.

Finally, the professor promotes another course that he offers, focusing on cryptography. It shows the connection between discrete mathematics and cryptography, emphasizing that the foundational concepts discussed in the previous course are applicable to this new subject. This encourages students to continue their learning journey.

Imagine a chef who specializes in desserts offering a class on how to make chocolate; it’s a natural follow-up for those who enjoyed learning about baking.

Second advertisement that I am always looking for motivated full time MS and PhD research scholars who want to work in cryptography.

The professor mentions that he is on the lookout for enthusiastic graduate students interested in pursuing research in cryptography. This serves as an invitation for students who wish to take their learning further into research.

Think of it like a coach seeking talented players to join a sports team; the professor is recruiting passionate scholars who can contribute to and learn from advanced research.

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