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04:22, 5 June 2025 Thakshashila talk contribs created page Neural Network (Created page with "= Neural Network = '''Neural Networks''' are a class of algorithms within Machine Learning and Deep Learning that are designed to recognize patterns. They are inspired by the structure and function of the biological brain and are used to approximate complex functions by learning from data. == Overview == A neural network consists of interconnected units (called '''neurons''' or '''nodes''') organized in layers. These layers process input data through weighted c...")
04:21, 5 June 2025 Thakshashila talk contribs created page Data Science (Created page with "= Data Science = '''Data Science''' is an interdisciplinary field that uses scientific methods, algorithms, and systems to extract knowledge and insights from structured and unstructured data. It integrates techniques from statistics, computer science, and domain-specific knowledge to turn raw data into actionable intelligence. == Overview == Data Science combines aspects of data analysis, machine learning, data engineering, and software development to address complex...")
04:20, 5 June 2025 Thakshashila talk contribs created page Deep Learning (Created page with "= Deep Learning = '''Deep Learning''' is a subfield of Machine Learning concerned with algorithms inspired by the structure and function of the brain, known as artificial neural networks. It is at the heart of many recent advances in Artificial Intelligence. == Overview == Deep learning models automatically learn representations of data through multiple layers of abstraction. These models excel at recognizing patterns in unstructured data such as images, audio,...")
04:20, 5 June 2025 Thakshashila talk contribs created page Artificial Intelligence (Created page with "= Artificial Intelligence = '''Artificial Intelligence (AI)''' is a branch of computer science that aims to create systems or machines that exhibit behavior typically requiring human intelligence. These behaviors include learning, reasoning, problem-solving, perception, language understanding, and decision-making. == Overview == Artificial Intelligence involves the design and development of algorithms that allow computers and software to perform tasks that would normal...")
04:18, 5 June 2025 Thakshashila talk contribs created page What is Machine Learning (Created page with "= What is Machine Learning = '''Machine Learning (ML)''' is a subfield of artificial intelligence (AI) that focuses on the development of systems that can learn from data and improve their performance over time without being explicitly programmed. == Overview == Machine Learning allows computers to recognize patterns, make decisions, and predict outcomes based on historical data. It contrasts with traditional programming, where rules and logic are manually coded. == T...")
04:54, 24 May 2025 Thakshashila talk contribs created page Problem: Find (A ∩ B) × (B ∩ C) (Created page with "= Problem: Find (A ∩ B) × (B ∩ C) = Given sets: <math>A = \{3, 5, 7\}</math> <math>B = \{7, 8\}</math> <math>C = \{8, 9\}</math> == Step 1: Find the Intersection A ∩ B == Intersection means elements common to both sets. Elements of A: 3, 5, 7 Elements of B: 7, 8 Common element is: <math>A \cap B = \{7\}</math> == Step 2: Find the Intersection B ∩ C == Elements of B: 7, 8 Elements of C: 8, 9 Common element is: <math>B \cap C = \{8\}</mat...")
04:54, 24 May 2025 Thakshashila talk contribs deleted page Problem 1 (content was: "= Problem: Find<math> \((A \cap B) \times (B \cap C)\)</math> = Given sets: <math> A = \{3, 5, 7\} \\ B = \{7, 8\} \\ C = \{8, 9\} </math> == Step 1: Find the Intersection \(A \cap B\) == The intersection of two sets contains all elements common to both sets. * Elements of \(A\) are: 3, 5, 7 * Elements of \(B\) are: 7, 8 Common elements: <math>A \cap...", and the only contributor was "Thakshashila" (talk))
04:53, 24 May 2025 Thakshashila talk contribs created page Problem 1 (Created page with "= Problem: Find \((A \cap B) \times (B \cap C)\) = Given sets: <math> A = \{3, 5, 7\} \\ B = \{7, 8\} \\ C = \{8, 9\} </math> == Step 1: Find the Intersection \(A \cap B\) == The intersection of two sets contains all elements common to both sets. * Elements of \(A\) are: 3, 5, 7 * Elements of \(B\) are: 7, 8 Common elements: <math>A \cap B = \{7\}</math> == Step 2: Find the Intersection \(B \cap C\) == * Elements of \(B\) are: 7, 8 * Elements of \(C\) are:...")
04:47, 24 May 2025 Thakshashila talk contribs created page Ahmed Zewail (Created page with "= Ahmed Zewail - The Father of Femtochemistry = '''Ahmed Hassan Zewail''' (1946–2016) was an Egyptian-American scientist known as the Father of Femtochemistry. He won the '''Nobel Prize in Chemistry''' in 1999 for his pioneering work on observing chemical reactions at extremely fast timescales. == Early Life and Education == * Born in Damanhur, Egypt, in 1946 * Studied at Alexandria University in Egypt * Completed his PhD at the University of Pennsylvania, USA...")
04:46, 24 May 2025 Thakshashila talk contribs created page Antoine Lavoisier (Created page with "= Antoine Lavoisier - The Father of Modern Chemistry = '''Antoine Laurent Lavoisier''' (1743–1794) was a French chemist who is widely regarded as the Father of Modern Chemistry. He revolutionized chemistry by introducing a scientific and quantitative approach to studying matter and chemical reactions. == Early Life and Education == * Born in Paris, France, in 1743 * Educated in science and law, but devoted his life to chemistry * Known for using careful measurem...")
04:44, 24 May 2025 Thakshashila talk contribs created page Marie Curie (Created page with "= Marie Curie - The Pioneer of Radioactivity = '''Marie Curie''' (1867–1934) was a world-renowned scientist known for her groundbreaking work on '''radioactivity'''. She was the first woman to win a Nobel Prize, and the only person to win Nobel Prizes in two different scientific fields — Physics and Chemistry. == Early Life and Education == * Born as '''Maria Sklodowska''' in Warsaw, Poland (1867) * Moved to Paris to study at the University of Paris (Sorbonne)...")
04:29, 24 May 2025 Thakshashila talk contribs created page Category:Chemistry (Created page with "= What is Chemistry? - Definition, Explanation, and Importance = '''Chemistry''' is the branch of science that studies the '''composition''', '''structure''', '''properties''', and '''changes of matter'''. It helps us understand how substances interact, combine, and change to form new substances. == Definition == Chemistry is the scientific study of: * What matter is made of (elements, atoms, molecules) * How substances behave and interact * How new materials are form...")
04:28, 24 May 2025 Thakshashila talk contribs created page Category:Mathematics (Created page with "= What is Mathematics? - Definition, Explanation, and Importance = '''Mathematics''' is the science of numbers, shapes, patterns, and logical reasoning. It helps us solve problems in daily life, science, business, and technology. == Definition == Mathematics is the study of: * '''Numbers''' and their operations (like addition, subtraction) * '''Shapes''' and space (geometry) * '''Patterns''' and sequences (algebra) * '''Measurements''' and quantities * '''Logical thin...")
04:27, 24 May 2025 Thakshashila talk contribs created page Category:Physics (Created page with "= What is Physics? - Definition, Explanation, and Importance = '''Physics''' is the branch of science that deals with the study of the '''natural world''', focusing on the '''matter''', '''energy''', and the '''laws that govern their behavior''. It tries to answer questions like: * How do objects move? * Why do things fall? * What is light? * How is electricity generated? * What causes sound? == Definition == Physics is the scientific study of '''matter''', '''energy...")
04:24, 24 May 2025 Thakshashila talk contribs created page Cartesian Product (Created page with "= Cartesian Product - Definition, Explanation, and Examples = The '''Cartesian Product''' is an operation used in mathematics to combine two sets and form a new set made of ordered pairs. This concept is widely used in set theory, coordinate geometry, and computer science. == Definition == If <math>A</math> and <math>B</math> are two sets, the '''Cartesian product''' of <math>A</math> and <math>B</math> is the set of all ordered pairs where: - The first element is fr...")
04:22, 24 May 2025 Thakshashila talk contribs created page Cartesian Product of Two Sets (Created page with "= Cartesian Product of Two Sets - Definition and Step-by-Step Examples = The [[Cartesian Product]] of two sets is the set of all possible '''ordered pairs''' where the first element comes from the first set and the second element comes from the second set. == Definition == If <math>A</math> and <math>B</math> are two sets, then the Cartesian Product of <math>A</math> and <math>B</math>, denoted by <math>A \times B</math>, is defined as: <math> A \times B...")
04:18, 24 May 2025 Thakshashila talk contribs created page Ordered Pairs in set (Created page with "= Ordered Pairs - Definition and Examples = An '''ordered pair''' is a fundamental concept in mathematics used to represent two elements together with an order that matters. It is usually written as <math>(a, b)</math>, where <math>a</math> is called the '''first element''' and <math>b</math> is the '''second element'''. == Key Points == * Unlike sets, the order of elements in an ordered pair is important. * Two ordered pairs <math>(a, b)</math> and <math>(c, d)</ma...")
04:16, 24 May 2025 Thakshashila talk contribs created page De Morgan (Created page with "= Augustus De Morgan - Mathematician Behind De Morgan's Laws = '''Augustus De Morgan''' (1806–1871) was a British mathematician and logician known for his pioneering work in formalizing logic and mathematics. He is famous for formulating the laws that bear his name, called De Morgan's Laws, which are fundamental in set theory, logic, and computer science. == Early Life and Education == - Born in India in 1806, De Morgan moved to England at a young age. - H...")
04:15, 24 May 2025 Thakshashila talk contribs created page De Morgan’s Laws (Created page with "= De Morgan's Laws - Definition, Explanation, and Examples = '''De Morgan''''s laws are fundamental rules in set theory that describe the relationship between union, intersection, and complements of sets. They help simplify complex set expressions, especially involving complements. == Statements of De Morgan's Laws == Let <math>A</math> and <math>B</math> be two sets and <math>U</math> be the universal set. 1. The complement of the union of two sets is equal to t...")
04:07, 24 May 2025 Thakshashila talk contribs created page Distributive Law of Sets (Created page with "= Distributive Law of Sets - Definition, Explanation, and Examples = The '''distributive law''' shows how union and intersection operations distribute over each other. It is a key property in set theory that helps simplify expressions involving both operations. == Distributive Law of Intersection over Union == For any three sets <math>A</math>, <math>B</math>, and <math>C</math>: <math> A \cap (B \cup C) = (A \cap B) \cup (A \cap C) </math> This means the intersecti...")
03:55, 24 May 2025 Thakshashila talk contribs created page Associative Law of Sets (Created page with "= Associative Law of Sets - Definition, Explanation, and Examples = The '''associative law''' is a fundamental property of set operations which states that when performing the same operation multiple times, the grouping (or association) of sets does not affect the result. == Associative Law for Union == For any three sets <math>A</math>, <math>B</math>, and <math>C</math>: <math> (A \cup B) \cup C = A \cup (B \cup C) </math> This means that whether you first unite <...")
03:47, 24 May 2025 Thakshashila talk contribs created page Commutative law on sets (Created page with "= Commutative Law of Sets - Definition, Explanation, and Examples = The '''commutative law''' is an important property of some set operations, meaning the order in which we perform the operation does not affect the result. == Commutative Law for Union == For any two sets <math>A</math> and <math>B</math>, the union operation is commutative. This means: <math> A \cup B = B \cup A </math> In words, combining set <math>A</math> with set <math>B</math> is the same as co...")
03:46, 24 May 2025 Thakshashila talk contribs created page Complement of a Set (Created page with "= Complement of a Set - Definition, Explanation, and Examples = The '''complement''' of a set contains all elements that are not in the set but belong to a larger, universal set. It helps identify what is "outside" a given set within a specified context. == Definition of Complement == Let <math>U</math> be the universal set, which contains all elements under consideration. The complement of a set <math>A</math>, denoted by <math>A'</math> or <math>\overline{A}</math>,...")
03:45, 24 May 2025 Thakshashila talk contribs created page Difference of Sets (Created page with "= Difference of Sets - Definition, Explanation, and Examples = The '''difference''' of two sets is an operation that finds elements that belong to one set but not the other. It is also called the '''relative complement'''. == Definition of Difference == The difference of sets <math>A</math> and <math>B</math>, denoted by <math>A - B</math>, is the set of all elements that are in <math>A</math> but not in <math>B</math>. Mathematically: <math>A - B = \{ x : x \in A \...")
03:44, 24 May 2025 Thakshashila talk contribs created page Intersection of Sets (Created page with "= Intersection of Sets - Definition, Explanation, and Examples = The '''intersection''' of two sets is an important set operation that finds all elements common to both sets. == Definition of Intersection == The intersection of two sets <math>A</math> and <math>B</math> is the set containing all elements that are in both <math>A</math> and <math>B</math>. It is denoted by: <math>A \cap B</math> Mathematically: <math>A \cap B = \{ x : x \in A \text{ and } x \in B \}...")
03:43, 24 May 2025 Thakshashila talk contribs created page Union of Sets (Created page with "= Union of Sets - Definition, Explanation, and Examples = The '''union''' of two sets is a fundamental operation in set theory. It combines all the elements from both sets into one set without repeating any element. == Definition of Union == The union of two sets <math>A</math> and <math>B</math> is the set containing all elements that belong to either <math>A</math>, or <math>B</math>, or both. It is denoted by: <math>A \cup B</math> Mathematically: <math>A \cup B...")
03:42, 24 May 2025 Thakshashila talk contribs created page Operations on sets (Created page with "= Operations on Sets - Overview and Basic Definitions = '''Operations on sets''' are procedures that combine or modify sets to form new sets. They are fundamental in set theory and are widely used in mathematics, computer science, and logic. == Basic Set Operations == Here are the most common operations on sets with brief explanations: * '''Union (∪)''': The union of two sets <math>A</math> and <math>B</math> is the set of all elements that are in <math>A</math> or...")
03:40, 24 May 2025 Thakshashila talk contribs created page Universal set (Created page with "= Universal Set - Definition and Examples = In set theory, the '''universal set''' is the set that contains '''all possible elements''' under consideration for a particular discussion or problem. It serves as the '''reference set''' or '''universe''' of discourse. == Definition of Universal Set == The '''universal set''' is usually denoted by <math>U</math>. It contains every element relevant to the context or subject being studied. For example, if we are discussing...")
03:38, 24 May 2025 Thakshashila talk contribs created page Proper subset (Created page with "= Proper Subset - Definition and Examples = A '''proper subset''' is a special kind of subset where all elements of one set are contained in another set, but the two sets are not equal. In other words, the proper subset must have fewer elements than the original set. == Definition of Proper Subset == A set <math>A</math> is called a '''proper subset''' of a set <math>B</math> if: * Every element of <math>A</math> is in <math>B</math>, and * <math>A</math> is not equa...")
03:37, 24 May 2025 Thakshashila talk contribs created page Subsets (Created page with "= Subsets - Definition, Types, and Examples = In set theory, a '''subset''' is a set whose elements all belong to another set. Subsets are fundamental in understanding the relationships between sets. == Definition of Subset == A set <math>A</math> is called a '''subset''' of a set <math>B</math> if every element of <math>A</math> is also an element of <math>B</math>. This is written as: <math>A \subseteq B</math> This means: <math>\forall x (x \in A \Rightarrow x \i...")
03:34, 24 May 2025 Thakshashila talk contribs created page Equal Sets (Created page with "= Equal Sets - Definition and Examples= In set theory, '''equal sets''' are sets that contain the '''exact same elements'''. The order of elements or how they are written does not matter, only the content does. == Definition of Equal Sets == Two sets A and B are said to be '''equal''' if they have '''exactly the same elements'''. This means every element of set A is in set B, and every element of set B is in set A. * Mathematically: <math>A = B \iff (x \in A \Rightar...")
03:34, 24 May 2025 Thakshashila talk contribs created page Singleton Set (Created page with "= Singleton Set - Definition and Examples = A '''singleton set''' is a special type of set that contains '''only one element'''. It is the smallest possible non-empty set in set theory. == Definition of a Singleton Set == A set that has '''exactly one element''' is called a '''singleton set'''. It is also known as a '''unit set'''. * In mathematical notation: <math>A = \{a\}</math> is a singleton set, because it contains only one element, '''a'''. == Characteristics...")
03:33, 24 May 2025 Thakshashila talk contribs created page Empty Set (Created page with "= Empty Set (Null Set) - Definition and Examples = The '''empty set''', also known as the '''null set''', is one of the most basic and important concepts in set theory. It refers to a set that '''contains no elements'''. It is often the starting point for understanding how sets behave. == Definition of Empty Set == An '''empty set''' is a set that has '''no elements''' in it. It is represented by: * <math>\emptyset</math> (the Greek letter phi) * or <math>\{\}</math...")
03:30, 24 May 2025 Thakshashila talk contribs created page Infinite Set (Created page with "= Infinite Set - Definition, Examples and Comparison = An '''infinite set''' is a set that contains an '''unlimited or uncountable number of elements'''. Unlike finite sets, infinite sets cannot be completely listed because they go on forever. == Definition of an Infinite Set == A set is called an '''infinite set''' if the number of its elements is '''not countable'''. In other words, it is impossible to list all the elements of the set completely, as they continue i...")
03:29, 24 May 2025 Thakshashila talk contribs created page Finite Set (Created page with "= Finite Set - Definition, Examples and Properties = A '''finite set''' is a type of set in mathematics that contains a '''countable number of distinct elements'''. This means the number of elements in the set is '''limited''' or '''fixed'''. Set theory often begins with understanding the concept of finite and infinite sets. == Definition of a Finite Set == A set is called a '''finite set''' if the number of elements in the set is '''countable''' and the process of li...")
03:25, 24 May 2025 Thakshashila talk contribs created page Introduction to Set theory (Created page with "= Introduction to Set Theory = Set theory is a fundamental topic in mathematics that deals with the study of '''sets''', which are collections of '''distinct''' and '''well-defined objects'''. It is the foundation for many advanced topics in mathematics and logic. == What is a Set? == A '''set''' is a collection of objects, called '''elements''' or '''members''', that are grouped together because they share a common property. * Example: A set of vowels in the English...")
08:05, 23 May 2025 Thakshashila talk contribs created page Matrix Addition (Created page with "= Matrix Addition = Matrix addition is the process of adding two matrices of the '''same dimensions''' by adding their corresponding elements. == Conditions for Matrix Addition == Two matrices can be added only if they have the same number of rows and the same number of columns. For example, if: * Matrix A is of order 2×3 * Matrix B must also be of order 2×3 to be added to A == Rule for Addition == If: <math> A = [a_{ij}], \quad B = [b_{ij}] </math> Then: <math>...")
08:03, 23 May 2025 Thakshashila talk contribs created page Matrix (Created page with "= Matrix and Its Types = A '''matrix''' is a rectangular arrangement of numbers, symbols, or expressions, organized in rows and columns. It is usually enclosed in square brackets like this: <math> A = \begin{bmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m1} & a_{m2} & \cdots & a_{mn} \end{bmatrix} </math> where <math>m</math> is the number of rows and <math>n</math> is the number of columns....")
08:02, 23 May 2025 Thakshashila talk contribs created page Basics of Calculus (Created page with "= Basics of Calculus = '''Calculus''' is a branch of mathematics that studies how things change. It helps us understand motion, growth, and areas under curves. Calculus is divided mainly into two parts: '''Differential Calculus''' and '''Integral Calculus'''. == Differential Calculus == Differential Calculus focuses on the concept of the '''derivative''', which represents the rate at which a quantity changes. For example, it tells us how fast a car is moving at any in...")
07:58, 23 May 2025 Thakshashila talk contribs created page File:Kbaselogo.png
07:58, 23 May 2025 Thakshashila talk contribs uploaded File:Kbaselogo.png
07:38, 23 May 2025 Thakshashila talk contribs created page Michael Faraday (Created page with "= Michael Faraday = '''Michael Faraday''' (22 September 1791 – 25 August 1867) was an English scientist who made foundational contributions to the fields of '''electromagnetism''' and '''electrochemistry'''. Though largely self-taught, Faraday is regarded as one of the greatest experimental physicists in history. == Early Life and Education == Faraday was born into a poor family in Newington Butts, now part of South London. He had little formal education and worked...")
07:34, 23 May 2025 Thakshashila talk contribs created page James Clerk Maxwell (Created page with "= James Clerk Maxwell = '''James Clerk Maxwell''' (13 June 1831 – 5 November 1879) was a Scottish physicist and mathematician who made profound contributions to the field of electromagnetism, thermodynamics, and optics. He is best known for formulating the set of equations that describe classical electromagnetism, known today as '''Maxwell's Equations'''. == Early Life and Education == Maxwell was born in Edinburgh, Scotland. From an early age, he demonstrated a str...")
07:30, 23 May 2025 Thakshashila talk contribs created page Ampère-Maxwell Law: (Created page with "= Ampère-Maxwell Law = The '''Ampère-Maxwell Law''' is one of the four equations in the set of '''Maxwell's Equations''', which form the foundation of classical electrodynamics. It is a generalization of Ampère's Law, accounting for the contribution of the changing electric field to the magnetic field. == Statement of the Law == In differential form, the Ampère-Maxwell Law is expressed as: <math> \nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0 \varepsilon_0 \...")
07:28, 23 May 2025 Thakshashila talk contribs created page Faraday's Law of Induction: (Created page with "= Faraday's Law of Induction: Definition and Mathematical Representation = == Introduction == '''Faraday’s Law of Electromagnetic Induction''' is a fundamental principle of electromagnetism discovered by Michael Faraday. It describes how a changing magnetic field within a closed loop induces an electromotive force (EMF) in the conductor. This principle is the working mechanism behind electric generators, transformers, and inductors. == Statement of Faraday’s Law ==...")
07:25, 23 May 2025 Thakshashila talk contribs created page Gauss's Law (Magnetic): (Created page with "= Gauss's Law (Magnetic): Definition and Mathematical Representation = == Introduction == '''Gauss’s Law for Magnetism''' is one of the four fundamental Maxwell's Equations in electromagnetism. It states that the total magnetic flux through any closed surface is zero, implying that magnetic monopoles do not exist (i.e., every magnetic field line that enters a surface also exits it). == Mathematical Formulation == === Integral Form === <math> \oint_{\text{closed...")
07:24, 23 May 2025 Thakshashila talk contribs created page Gauss's Law (Electric): (Created page with "= Gauss's Law (Electric): Definition and Mathematical Representation = == Introduction == '''Gauss’s Law''' is a fundamental law in electrostatics that relates the electric flux through a closed surface to the total electric charge enclosed by that surface. It is one of the four equations in Maxwell's Equations and provides a powerful method for calculating electric fields, especially with high symmetry. == Mathematical Formulation == === Integral Form === <math...")
07:18, 23 May 2025 Thakshashila talk contribs created page Electromagnetism (Created page with "= Electromagnetism: Definition and Mathematical Representation = == Introduction == '''Electromagnetism''' is a fundamental branch of physics that deals with the study of electric and magnetic fields and their interactions with matter. It is one of the four fundamental forces of nature and is described by the unified theory of electricity and magnetism, primarily governed by Maxwell’s equations. Electromagnetic phenomena are the basis for many modern technologies inc...")
07:15, 23 May 2025 Thakshashila talk contribs created page Quantum (Created page with "= Quantum: Definition and Mathematical Representation = == Introduction == In physics, the term '''quantum''' refers to the smallest possible discrete unit of any physical property. The concept originates from '''quantum mechanics''', a fundamental theory that describes the behavior of matter and energy on atomic and subatomic scales. The term "quantum" (plural: "quanta") was first introduced in the early 20th century to explain phenomena that classical physics could n...")
07:14, 23 May 2025 Thakshashila talk contribs created page Wave (Created page with "= Wave: Definition and Mathematical Representation = == Introduction == In physics, a '''wave''' is a disturbance or oscillation that travels through space and matter, transferring energy from one point to another without the permanent displacement of the medium. Waves are classified into different types based on the direction of particle motion and the medium through which they propagate. == Types of Waves == === 1. Mechanical Waves === Require a medium to propagate....")