Blog
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In the previous post, we explored the semantics of propositional logic using truth tables to determine the truth values of logical expressions. While truth tables are useful for evaluating small formulas, they become impractical for complex logical statements. Instead, formal proof techniques allow us to establish the validity of logical statements using deductive reasoning. This… Continue reading.
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Why do physicists and mathematicians value elegance and simplicity in their theories? Is beauty in science merely an aesthetic preference, or does it point to something fundamental about reality? Throughout history, scientists and philosophers have debated whether mathematical elegance is a reflection of nature’s inherent structure or simply a tool that helps us organize our… Continue reading.
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In the previous post of this thread, we examined the syntax of propositional logic, focusing on how logical statements are constructed using propositions and logical connectives. Now, we turn to the semantics of propositional logic, which determines how the truth values of logical expressions are evaluated. This is achieved using truth tables, a fundamental tool… Continue reading.
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One of the fundamental differences between C++ and many modern programming languages is that C++ is a compiled language. In languages like Python, code is executed line by line by an interpreter, allowing you to write and run a script instantly. In C++, however, your code must be compiled into an executable file before it… Continue reading.
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When it comes to scientific computing, Python and C++ are two of the most widely used programming languages. Each has its own strengths and weaknesses, making them suitable for different types of computational tasks. In this post, I will compare these languages, discuss essential libraries, and outline a basic workflow for implementing numerical methods in… Continue reading.
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Quantitative finance relies on a combination of mathematics, statistics, and computational tools to develop models and strategies for financial decision-making. As a quant, mastering these tools is essential to effectively analyze financial data, implement models, and automate trading or risk management processes. While I will assume familiarity with these concepts for now, I will cover… Continue reading.
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Classical mechanics is one of the oldest and most profound branches of physics, shaping our understanding of motion and forces while laying the foundation for modern physics. The journey of mechanics spans centuries, from ancient philosophical discussions about motion to the rigorous mathematical frameworks of today. Understanding its historical evolution not only deepens our appreciation… Continue reading.
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What is the connection between scientific theories and reality? Are the models we create accurate reflections of an underlying truth, or are they merely useful constructs that help us navigate the world? These are fundamental questions in both philosophy of science and epistemology, and they shape the way we think about knowledge itself. Scientific Theories… Continue reading.
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In the previous post of this thread, we introduced propositional logic and its purpose: to provide a formal system for analyzing and evaluating statements using logical structures. Now, we turn to the syntax of propositional logic, which defines the fundamental building blocks of this system. Propositions and Atomic Statements At the heart of propositional logic… Continue reading.
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In the previous post in this thread, we explored the foundations of mathematics and the importance of formalism in ensuring mathematical consistency and rigor. We also introduced the role of logic as the backbone of mathematical reasoning. Building on that foundation, we now turn to propositional logic, the simplest and most fundamental form of formal… Continue reading.
