Blog
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Humans have always sought knowledge, driven by an insatiable curiosity that compels us to explore, learn, and question. From ancient civilizations charting the stars to modern scientists probing the quantum world, our relentless desire to understand our surroundings defines us uniquely among Earth’s creatures. Unlike most animals, whose curiosity fades with maturity, humans maintain a… Continue reading.
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Before we delve deeper into predicate logic, it’s important to clarify a few essential concepts from set theory. Predicate logic itself relies on some basic set-theoretic notions for its formal definitions and interpretations. This short introduction provides the minimal set theory you’ll need. Introduction to Sets A set is a collection of distinct objects, called… Continue reading.
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In my previous post of this thread, I introduced the basic structure of a simple C++ program. Before moving on to more advanced topics like memory management, pointers, and references, I want to cover a fundamental concept: variables. Variables are an essential building block of programming. They let you store, access, and manipulate data in… Continue reading.
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Numerical computations inherently involve errors due to the limitations of representing and manipulating numbers in a finite-precision system. Understanding the different types of numerical errors is crucial for developing stable and accurate numerical algorithms. In this post, I will discuss three primary sources of numerical errors: round-off errors, truncation errors, and numerical stability. Round-Off Errors… Continue reading.
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In financial modeling, randomness plays a crucial role. Prices, interest rates, and volatility evolve over time in ways that are inherently unpredictable. To model these dynamics mathematically, we turn to stochastic processes, which provide a framework for describing random changes over time. Among these, Brownian motion is the cornerstone of many financial models, particularly for… Continue reading.
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In the previous post of this series, we explored Newton’s laws of motion, which describe how objects move under the influence of forces. However, these laws assume that we are observing motion from an appropriate reference frame—a perspective from which positions, velocities, and accelerations are measured. Not all reference frames are equivalent when applying Newton’s… Continue reading.
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In the previous posts, we’ve extensively discussed propositional logic, exploring its syntax, semantics, and proof techniques. Propositional logic is powerful and foundational; however, it has significant limitations in its expressiveness. Recognizing these limitations is essential to understanding why more advanced logical systems, such as predicate logic, are necessary. Expressiveness Limitations Propositional logic deals exclusively with… Continue reading.
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In the quest to comprehend the universe, scientists and philosophers have long grappled with the concept of emergence—the phenomenon where complex systems and patterns arise from the interaction of simpler elements. This notion challenges traditional reductionism, which posits that understanding the fundamental components of a system suffices to explain the whole. Emergence suggests that there… Continue reading.
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In previous posts of this thread, we introduced formal proof techniques in propositional logic, discussing natural deduction, Hilbert-style proofs, and the fundamental concepts of soundness and completeness. Now, we turn to advanced proof strategies that enhance our ability to construct and analyze proofs efficiently. In particular, we will explore proof by contradiction and resolution, two… Continue reading.
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In the previous post, I introduced how C++ programs are compiled, executed, and how they manage memory. Now it’s time to write your very first C++ program! By the end of this post, you will have compiled and executed your first working C++ program and understood its fundamental structure. Let’s dive in. Writing and Compiling… Continue reading.
