Introduction

This blog is for students who are interested in understanding the fundamental subjects of computer science and seeing how these core areas connect to advanced research topics, modern technologies, large language models (LLMs), and the cutting-edge work happening in the field of AI and beyond. Our expert, Mr. VK, is doing his Ph.D. from IIT Roorkee and has a strong background in basic computer science areas. He will explain why subjects like theory of computation, data structures, algorithms, discrete mathematics, and graph theory are so important. He will also talk about how these subjects relate to the modern world of AI, large language models, and advanced research. In addition, he will share insights into his own research area, which deals with large graphs and influence maximization. Finally, he will give advice to students on what they should study and focus on as the field of computer science rapidly evolves.

Key Computer Science Subjects and Their Importance

Theory of Computation:

Mr. VK suggests subjects like theory of computation as one of the core computer science areas. In theory of computation, students learn about different classes of languages. They start from regular expressions and regular languages, then move on to context-free languages, context-sensitive languages, and at the end, they study Turing machines. These are the main concepts in theory of computation that are usually taught in bachelor’s programs.

He explains that theory of computation helps in understanding how machines process languages and what kinds of problems are computable. By starting from simple concepts like regular expressions and moving all the way up to Turing machines, students learn how the hierarchy of languages and computational models is built. This background helps one understand how programming languages and compilers break down code into tokens and parse them, and how everything eventually translates into machine-level instructions. Theory of computation basically tells us about the fundamental limits of what machines can do and how they recognize patterns and languages.

Algorithms:

Regarding algorithms, Mr. VK says that algorithms tell us how the machine works and how we can make it work more efficiently. An algorithm is a set of instructions to do a particular task, and for any given task, there can be multiple ways to do it. Algorithms help us find the most efficient way. The reason we study different algorithms is to optimize time and computation, making the machine do tasks in a more efficient manner.

He gives examples like when finding a path between two nodes in a graph, there can be different algorithms to do that. One researcher might propose an algorithm, another might improve it, and so on. The goal is to reduce the time or resources needed. Key algorithms that students encounter early on include searching and sorting algorithms such as insertion sort, merge sort, quick sort, heap sort—these show how we can rearrange arrays. Then there are algorithms related to graphs, like Prim’s and Kruskal’s algorithms for finding minimum spanning trees, and Dijkstra’s shortest path algorithm. These algorithms show how to find the shortest path from one point to another. By studying algorithms, we learn how to make machines more efficient, which is a core concept in computer science.

Data Structures:

Data structures, according to Mr. VK, mainly tell us about the different ways we can store data in our system. We have various methods of storing data: arrays, linked lists, stacks, queues, and trees. Each data structure has its own advantages and disadvantages, and the choice depends on what we need to do.

He describes how we start with arrays, then move on to linked lists, which is another way of putting data in a system, and then to stacks and queues. Each data structure allows certain operations (like push and pop in stacks) and we have to understand the pros and cons. Trees, including binary trees, red-black trees, and others, provide hierarchical ways of storing data. All these data structures help us store and retrieve data efficiently depending on the conditions of the problem we are trying to solve. The reason we study them is to match the problem’s requirements with the characteristics of the data structure that can handle those operations efficiently.

Graph Theory:

Mr. VK emphasizes the importance of graph theory. He explains that graph theory is crucial because every problem can be decomposed into a graph form. For example, consider a large system like Facebook. Each person can be represented as a node, and an edge between two nodes can represent a friendship. Thus, the entire social network can be seen as a huge graph.

By applying graph properties, we can find out various things. For instance, the degree of a node tells us how many friends a person has. Graph theory is also used in real-world problems like Google Maps, where each place can be a node and roads are edges, and we need to find the shortest path to travel from one point to another. Graph theory is very realistic and is used every day in many spheres of life.

In terms of key topics, Mr. VK mentions that in graph theory, we start from the basics: learning about nodes, edges, degrees of nodes, and the handshaking lemma. Then we learn about different kinds of graphs, such as Hamiltonian graphs, Euler graphs, star graphs, and concepts like the centroid and diameter of a graph. These concepts help us understand the structure and properties of the graph we are dealing with.

Discrete Mathematics:

Mr. VK also mentions discrete mathematics as one of the core subjects. He explains the difference between discrete and continuous. Discrete means things are separate and not connected continuously. Discrete mathematics deals with topics like recurrence relations, polynomials in recurrence relations, characteristic equations, and using algebraic methods to solve these equations.

He points out that graph theory is also a part of discrete mathematics. Some probability concepts like random variables come under discrete mathematics as well. Mathematical induction is another topic in discrete math that helps us prove the correctness of theorems or formulas by showing they are true for the base case and then proving that if it’s true for one case, it’s true for the next.

Mr. VK says that 50 years ago, there was no separate field called computer science—everything was maths. The early computer scientists were mathematicians who tried to break down problems into known mathematical concepts. Discrete math, graph theory, and other such areas have a long history dating back to Euler in the 16th or 17th century (he mentions these historical roots), who formulated problems that later became the foundation of graph theory. Thus, to understand computer science deeply, we must understand discrete mathematics because computer science originated and evolved from mathematical concepts.

He also mentions a reference to the Rosen book for discrete mathematics, stating that every exercise in that book has some programming exercise associated with it. This shows how closely discrete mathematics and computer science are linked.

Mr. VK’s Research Area

When asked about his research, Mr. VK says he works on complex analysis of very big graphs and networks. He clarifies that it’s not “computer networks” in the traditional sense, but rather modeling a problem as a very large graph with millions of nodes. He focuses on a concept known as influence block maximization.

He gives a basic overview: imagine you have data of people on Twitter (like 100 million people), and you need to sell a product. You cannot go to each person and say, “buy my product.” Instead, what companies do is give the product to a selected set of people—some initial nodes, often influential ones—and these people share or advertise the product. The information propagates through the network from node to node. The question is: which initial nodes should we pick to maximize the spread of information?

This is called the influence maximization problem. The idea is if someone is very influential (like a celebrity with 1 million followers), giving them the product to advertise can spread the word quickly. The information then moves from one node to another node, eventually reaching many people.

This problem is not limited to marketing. It can also apply to epidemiology, like in the case of diseases spreading. If we represent people as nodes and connections as edges, we can study how a disease propagates. By identifying certain initial nodes (like “patient zero”), we can see how the disease spreads and predict outcomes.

So Mr. VK’s research is about understanding graph information diffusion and finding strategies to maximize influence in these large-scale networks.

Modern Developments: LLMs, AI, and Changing Landscape

Mr. VK then shifts to discussing current trends. He says that currently, if students are doing their bachelor’s, the field of LLMs (Large Language Models) is evolving very fast. We have heard about AI and machine learning for the past 15 years, but now the game has changed after the introduction of LLMs, such as ChatGPT and other GPT models. Research teams at places like DeepMind are publishing high-quality research papers, and we are in a sort of race for AI dominance.

Nvidia is also heavily involved in model training. The complexity and sophistication of models have increased. Back in 2015 or 2016, people were mainly dealing with linear regression, supervised learning, and unsupervised learning. Now, the fields have expanded into deep learning, graph neural networks, and natural language processing at a much more complex scale.

He mentions the awarding of two Nobel Prizes in fields that connect with the advancements in computer science and AI. One significant development is AlphaFold by Google DeepMind. AlphaFold can predict protein structures with very high accuracy (96–97%), something that used to be very computationally expensive and time-consuming. Before AlphaFold, only about 200k protein structures out of a possible 200 million were known. AlphaFold uses AI to predict new protein structures, accelerating research in biology, chemistry, and medicine.

He explains that understanding protein structures can help us figure out why some animals (like sharks) do not get cancer, which could lead to breakthroughs in health and disease prevention. AlphaFold and related work received huge recognition because it made a giant leap in how we study proteins and can help in understanding complex diseases, how cancer cells work, and in drug discovery.

Mr. VK says that these are the different domains that students should look into right now if they are in computer science. Because we are at the budding phase of AI, 10 or 20 years from now things will be entirely different. We might create movies with the help of AI, or use AI to prove mathematical theorems that have been unproven for hundreds of years. People are already working on these problems, and AI’s implications are vast.

Connecting Core Computer Science Subjects to LLMs and AI

Mr. VK then addresses how the basic computer science subjects connect to these advanced fields like LLMs and AI. He says that, for example, theory of computation teaches us about languages and models like NFA (Nondeterministic Finite Automata), PDA (Pushdown Automata), and Turing machines. These help us understand how computers parse instructions and code. Understanding these fundamental concepts gives us the background to comprehend how advanced AI models process language and data internally.

Without a strong background in these core areas—like probability, summation, integration, and discrete math—it becomes difficult to read advanced research papers, many of which contain complex mathematics. Also, people involved in deep research generally have strong mathematical and theoretical backgrounds. If you are not sound in your basics, you will not be able to fully grasp these high-level concepts or contribute at that level.

He emphasizes that everything starts from the smallest steps. If you don’t know how to write an algorithm or verify whether it is correct, it will not make sense to jump directly into advanced AI. You must have a sound understanding of basic theory, algorithms, and math to read research papers and understand what these researchers are doing. The fundamentals provide the confidence and skill to tackle higher-level problems.

Advice to Students

At the end, Mr. VK advises upcoming students to study their core subjects in computer science thoroughly. He specifically mentions that currently the field of LLMs is evolving. Students should read some basic papers, watch videos, and connect with people working in these domains. He points out that we are at a starting phase of an AI race, and having a strong foundation will help students adapt to new technologies easily.

While AI, machine learning, and deep learning are hot topics, students should not forget that understanding how computers work at a basic level—through theory of computation, data structures, algorithms, discrete math, and graph theory—is crucial. These subjects will prepare them to understand and engage with complex AI models, graph neural networks, NLP techniques, and more. As time goes on, we will do things with AI that are unimaginable today, and being prepared with the fundamentals will let students be part of these future breakthroughs.

He also mentioned that the Nobel Prize recognition for AlphaFold’s contribution shows how AI and computer science concepts can lead to significant advancements in other fields like chemistry and biology. This demonstrates the interdisciplinary importance of a strong computer science foundation.

Conclusion

From theory of computation, data structures, algorithms, discrete mathematics, and graph theory to advanced fields like large language models, deep learning, and AI-driven biological discoveries, Mr. VK’s insights show that the fundamental subjects of computer science are not just academic exercises. They are essential tools that lay the groundwork for understanding and innovating in cutting-edge research and real-world applications.

His research on influence maximization in large graphs exemplifies how theoretical concepts directly apply to practical problems like marketing strategies or understanding epidemic spreads. The shift in computer science and AI over the last decade—from simple models to complex LLMs and breakthroughs like AlphaFold—highlights the need for a solid foundation. Students who invest time in these basics now will be well-equipped to engage with and shape the future of technology, AI, and interdisciplinary research.