Math Modeling Breakthroughs in Science and Tech

How to start your career in #Computational Science? If you want to enter computational mechanics, focus on fundamentals — not software tools. First → Master Linear Algebra. It is the language of simulations, machine learning, FEM, optimization — everything. Read Introduction to Linear Algebra by Gilbert Strang. For intuition, watch Essence of Linear Algebra by 3Blue1Brown. Second → Increase your typing speed. Your brain thinks fast. Your fingers should not slow you down. If your typing speed matches your thinking speed (around 80–100 WPM), your work becomes seamless. Third → Learn Numerical Methods deeply. Mathematics is continuous. Computers are discrete. Read Steven C. Chapra’s book on Numerical Methods and implement every algorithm yourself. Fourth → Understand how computers actually compute. Learn floating-point representation, precision, rounding errors, and machine epsilon. If you don’t understand numerical precision, you cannot build stable simulations. Computational science sits at the intersection of mathematics, algorithms, and computer architecture. Build the foundation first. Tools will follow. --- If you want to be part of this community and grow with us in 2026, join here: → https://lnkd.in/dR4U79su Let’s build this together.

Sharing a blog I wrote while studying simulation and numerical methods. It explores how Euler’s method translates instantaneous change into stepwise computation , the core mechanism that turns differential equations into simulations. A simple iterative idea, but foundational to modeling, optimization, and machine learning. Would love to hear your thoughts.

Design better simulations—and understand why they matter! Join Center for Targeted Machine Learning and Causal Inference (CTML) on Wednesday, February 18th for “Simulations Done Right,” a workshop with Alejandro Schuler, CTML Faculty. This workshop will take place at 12:00 PM in Berkeley Way West, 5th Floor, Room 5401. Abstract: Simulation studies are ubiquitous in statistical research and practice, but students are rarely given formal training in how to design them. Since they are not glamorous, many advisors are happy to delegate them entirely to students, providing little guidance (I count myself as accused!). As a result, many simulation studies fail to address relevant questions, are more complicated and computationally intensive than they need to be, contain bugs, or are not properly described. In this workshop, students will first learn how to formulate goals for their simulations in the context of their research project and overall rhetorical aims. In particular, we will discuss how theoretical understanding helps to define simulation goals and how carefully iterating between simulation (empirical verification) and theory-building is the basis of scientific understanding. We will then discuss how to implement simulations so that they address goals while being as lightweight as possible, since the ability to quickly iterate on bugs and theory-building is key to being productive and staying engaged. Lastly, students will learn how to write about their simulations in a structured format so that it is clear to readers what the goals are and whether they have been accomplished.

Visualizing scalars, vectors, matrices, and tensors is key to understanding modern mathematics and machine learning. Fluxion enables clear, animated representations of these concepts-built with a growing community focused on learning and experimentation. #FluxionEngine #LinearAlgebra #Mathematics #Visualization #STEM #DataScience #CommunityDriven

Think Beyond Limits. Turn Data into Insight. Build the Future. Happy to share that my research paper “Advanced Machine Learning Approaches for Prediction of Compressive Strength of Sustainable Concrete” has been published in International Journal of Scientific Research in Engineering and Management (IJSREM), March 2026 (Volume 10, Issue 03). This study explores how machine learning models can be applied to engineering materials by comparing algorithms such as Random Forest, Gradient Boosting, XGBoost, AdaBoost, and Multiple Linear Regression for predicting concrete strength. Working on this research helped me strengthen my understanding of data-driven engineering, model evaluation, and real-world machine learning applications. Looking forward to continuing my journey in machine learning, research, and sustainable engineering solutions. #Research #MachineLearning #CivilEngineering #DataScience #EngineeringInnovation

📘 What is a System of Equations? It’s not just math. It’s structured thinking. A system of equations is when two or more equations work together to find a common solution. Example: x + y = 10 x − y = 2 Solve them together → x = 6 y = 4 That point satisfies both equations Systems of equations power: • Engineering calculations • Business forecasting • AI models • Data science • Quantum algorithms In advanced mathematics, they become matrix equations — the foundation of modern computing. Math is not about numbers. It’s about solving real-world problems logically. #Mathematics #LinearAlgebra #ProblemSolving #AI #STEM #LearningJourney #FutureSkills

Code2Math: Multi-Agent Framework for Mathematical Problem Synthesis — code agents autonomously evolve mathematical problems into more complex variations, generating high-quality training data for reasoning models. Scaling math reasoning requires diverse, difficult problems. Code2Math leverages collaborative agents to programmatically generate and verify increasingly complex problem variations — a scalable approach to building reasoning training corpora. arXiv: 2603.03202 #MachineLearning #MathReasoning #SyntheticData

As part of my recent learning in simulation and numerical methods, I uncovered a deceptively simple idea.💡 We often build models that describe 𝘪𝘯𝘴𝘵𝘢𝘯𝘵𝘢𝘯𝘦𝘰𝘶𝘴 𝘤𝘩𝘢𝘯𝘨𝘦. But computers don’t think in instants, they think in 𝘴𝘵𝘦𝘱𝘴. So how do we turn smooth, continuous mathematics into something a machine can actually run? The key is surprisingly straightforward: break change into very small increments and move forward step by step. That subtle shift is exactly what 𝗘𝘂𝗹𝗲𝗿’𝘀 𝗠𝗲𝘁𝗵𝗼𝗱 does and it’s what transforms differential equations into simulations. It’s fascinating how such a simple idea forms the bridge between pure calculus and practical computation. #simulation #statistics #optimization #datascience

𝗘𝘃𝗲𝗿𝘆 𝗺𝗮𝗷𝗼𝗿 𝘀𝘆𝘀𝘁𝗲𝗺 𝗮𝗿𝗼𝘂𝗻𝗱 𝘆𝗼𝘂 𝗿𝘂𝗻𝘀 𝗼𝗻 𝗺𝗮𝘁𝗵𝗲𝗺𝗮𝘁𝗶𝗰𝘀. Interest rates. Engineering designs. Medical research. Climate models. Artificial intelligence. Math is not abstract. It is infrastructure. The difference between being affected by a system and designing a system is mathematical literacy. When you understand probability, you understand risk. When you understand algebra, you understand growth. When you understand data, you understand influence. Mathematics is power. And the more of it you master, the more choices you control. 1. Where do you see mathematics operating in your everyday life? 2. If you could master one math skill this year, what would it be? #Math #BlackMathGenius #LearnMath #MooreMathGeniuses

𝗘𝘃𝗲𝗿𝘆 𝗺𝗮𝗷𝗼𝗿 𝘀𝘆𝘀𝘁𝗲𝗺 𝗮𝗿𝗼𝘂𝗻𝗱 𝘆𝗼𝘂 𝗿𝘂𝗻𝘀 𝗼𝗻 𝗺𝗮𝘁𝗵𝗲𝗺𝗮𝘁𝗶𝗰𝘀. Interest rates. Engineering designs. Medical research. Climate models. Artificial intelligence. Math is not abstract. It is infrastructure. The difference between being affected by a system and designing a system is mathematical literacy. When you understand probability, you understand risk. When you understand algebra, you understand growth. When you understand data, you understand influence. Mathematics is power. And the more of it you master, the more choices you control. 1. Where do you see mathematics operating in your everyday life? 2. If you could master one math skill this year, what would it be? #Math #BlackMathGenius #LearnMath #MooreMathGeniuses