School Alive’s Post

Happy Pi Approximation Day! 🎉📐 Today, July 22, we celebrate the mathematical wonder of π (pi), a number that symbolizes the ratio of a circle’s circumference to its diameter. This date is special because 22/7 is a common approximation for π, and it beautifully connects with the spirit of mathematical exploration. 🥧 Pi is an irrational number, meaning it cannot be precisely expressed as a simple fraction, and its decimal representation continues infinitely without repeating. It starts with 3.14159... and extends beyond with endless digits, reflecting the boundless and enigmatic nature of mathematics. 🌌 While 22/7 provides a fairly good approximation, equating to approximately 3.14285714, it is important to note that it’s not an exact representation of π. For more accurate calculations, mathematicians often use fractions like 355/113, which is accurate to six decimal places (3.14159292). 📏🔢 Pi plays a crucial role in various fields, from geometry and trigonometry to physics and engineering. Its applications are vast and profound, influencing everything from the design of circular objects to complex calculations in theoretical physics. 🌍✨ Pi Approximation Day is a perfect opportunity to celebrate the beauty of numbers and the role they play in our lives. Whether you’re solving problems, exploring new mathematical concepts, or simply appreciating the elegance of π, today is a reminder of the joy and curiosity that math brings. Let’s embrace the mystery and wonder of this incredible number and continue to marvel at the endless possibilities that mathematics offers! #PiApproximationDay #MathMagic #CelebratePi #Mathematics #PiDay #CuriosityInMath #NumberFun

Access the complete PDF Solutions Manual for Finite Mathematics with Applications In the Management Natural and Social Sciences 13th Edition by Lial. Revamp your studying with our essential resources. #testbank #test_banks #solutions_manual

The Langlands conjecture is a part of the broader Langlands program, an ambitious and influential set of conjectures connecting number theory and representation theory. It proposes deep connections between Galois groups (related to symmetries in algebra) and automorphic forms (complex-analytic functions that are highly symmetric). The program aims to unify various branches of mathematics, including number theory, algebraic geometry, and harmonic analysis, by showing that these seemingly disparate areas are manifestations of the same underlying structures. A group of nine mathematicians has proved the geometric Langlands conjecture, a major part of the Langlands program, after 30 years of effort. The proof, spanning over 800 pages, links areas of number theory, geometry, and function fields, drawing analogies to Fourier analysis. Led by Dennis Gaitsgory and Sam Raskin, this achievement is described as creating a “rising sea” of ideas that will influence various mathematical domains. This work marks a significant milestone in understanding the geometric aspects of the Langlands program. For further details, you can read the full article on Quanta Magazine https://lnkd.in/ecm6W9Bg #Langlands conjecture

Greetings Network. I am thrilled to announce that I have published a new article about The Calculus of Variations (or Variational Calculus) on my physics/maths blog page, Physfrenzy. The research experience has been fulfilling and enlightening, revealing the wonderful extent to which mathematics can be applied to problems in the real world - now I wish to share this knowledge with anyone that is interested in and fascinated by the seemingly limitless possibilities of maths and its inextricable link to physics. The article contains (almost) everything about the Calculus of Variations at the fundamental level from theory and derivations, to real-world applications and worked solutions, and I hope that those of you that explore it find it enjoyable and illuminating. Some of the key topics covered include: ➡ Proving that the shortest path between two points (also called a geodesic) is a straight line. ➡ Finding the path of fastest descent (minimum time of journey) between two points for a particle travelling under the influence of gravity and without frictional forces - this is the famous "Brachistochrone Problem". ➡ Finding the shape that a flexible chain assumes when suspended, with supports holding it at each of its ends - this is the "Catenary Problem". ➡ Lagrangian Mechanics - a method of finding the equations of motion of a system using energy alone, without considering forces at all; this also works on the quantum level, in addition to its use in classical mechanics! Link to the article: https://lnkd.in/dP_4-c8g (DESKTOP/LAPTOP HIGHLY RECOMMENDED) Finally, I have also created a digital poster summarising the Calculus of Variations - DM me if you would like to receive one. Thank you for your support, and be sure to drop any feedback in the comment section - this would be appreciated.

1st Semester (January 2018 – April 2018) MATH 101 Differential & Integral Calculus   3 Credit Hours, 3 Contact Hours per Week   Differential Calculus: Limits, continuity and differentiability. Successive differentiation of various types of functions. Leibnitz’s theorem. Rolle’s theorem, Mean value theorem, Taylor’s and Maclaurin's theorems in finite and infinite forms. Cauchy’s form of remainders. Expansion of functions, evaluation of indeterminate forms of L’ Hospital’s rule. Partial differentiation. Euler’s theorem. Tangent and normal. Determination of maximum and minimum values of functions.   Integral Calculus: Integration by the method of substitution. Standard integrals. Integration by successive reduction. Definite integrals, its properties and use in summing series. Beta function and Gamma function. Area under a plane curve and area of a region enclosed by two curves in cartesian and polar co-ordinates. Volumes and surface areas of solids of revolution. 

It might seem that nothing happens during the summer, but hey, the geometric (unramified, categorical) Langlands conjecture has been proved, and that is huge. It took "only" 30 years of top level mathematics! Langlands conjectures create bridges between distant branches of mathematics and by doing so enable lots of very complex results to become tractable, and that's one of the reasons they are one of the most active areas of current research in mathematics. A well know example is how a restricted from of one of the conjectures (a special case of modularity of elliptic curves) allowed Andrew Wiles to prove Fermat's last theorem (than resisted attemps to prove it from many of the best mathematicians of three and a half centuries), but they go much, much further. Also, GLC has deep connections with current theoretical physics (particularily with M-theory, that is best described as "a theory that could explain everything, but currently explains nothing, by unifying many other previous theories that explained nothing but could have explained almost everything", and which was responsible for "the second superstring revolution") https://lnkd.in/ee65UP4a

🎲 Calculated Mathematics Microlesson 📈 ❓ What is the Pythagorean Theorem, and why is it important? 🙋 The Pythagorean Theorem is a fundamental formula in mathematics that relates the lengths of the sides of a right triangle. ⏳ Discovered by the ancient Greek mathematician Pythagoras, this theorem has been known and used for over 2,500 years. 💡 The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. It is expressed as (a^2 + b^2 = c^2), where “c” is the hypotenuse and “a” and “b” are the other two sides. 🔍 This theorem is crucial for solving problems in geometry, trigonometry, and algebra. It allows for the calculation of distance and the properties of shapes and forms the basis for many other mathematical concepts. 🌎 The Pythagorean Theorem is widely used in various fields, including architecture, engineering, astronomy, and computer science. It helps in designing buildings, navigating by GPS, and creating digital graphics. 🎯 Draw a right triangle and measure its sides. Apply the Pythagorean Theorem to check the relationship between the lengths of the sides. Experiment with different right triangles to see how the theorem consistently applies. #Mathematics #HAMSTER #SchoolAlive

MATHEMATICS-THE DEFINITION 1.Mathematics is the abstract science of number, quantity, and space. 2.It involves the study of patterns, structures, and relationships through logical reasoning and quantitative analysis. 3.Mathematics can be broadly divided into pure mathematics, which focuses on theoretical concepts and foundational principles, and applied mathematics, which uses these concepts to solve real-world problems in various fields such as engineering, physics, economics, and more. 4.It encompasses a wide range of topics including arithmetic, algebra, geometry, calculus, and statistics, among others.

Department of Mathematics for Excellence, Simats Engineering organizing a Series on Mathematics "Jesse Douglas: Pioneer in Geometry, Group Theory and the Calculus of Variations" on 03 July 2024 #simats #saveethabreeze #mhrdinnovationcell #iic #jessedouglas #geometry #grouptheory