Top Mathematics discussions
NishMath - #Applications
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Nigel Chaffey@Plant Cuttings - 75d
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What's new
, Terence Tao
Recent research highlights the mathematical principles underlying natural phenomena, including the spiral patterns observed in plant growth. A new book, "Do plants know math?", delves into the fascinating world of phyllotaxis, which is the arrangement of leaves on a plant stem. The book explores the connection between the positioning of leaves, scales on cones, and the patterning of flower heads with mathematical concepts like the Fibonacci sequence and divergence angles. These concepts are explained alongside other essential phyllotaxis terminology within the book, showcasing the technical nature of the subject.
In other mathematical developments, mathematicians are using quaternions to analyze spherical trigonometry. This involves an extension of complex numbers which are non-commutative. Quaternions have properties like associative multiplication and the existence of multiplicative inverses. The exploration of these mathematical constructs provide insights into rotations and relationships in space, adding another dimension to mathematical analysis. Additionally, basic mathematical concepts, such as place value and face value, are also being explored. Place value refers to the value of a digit based on its position in a number, while face value is simply the digit itself. Recommended read:
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@thequantuminsider.com - 70d
Recent breakthroughs in quantum research are showing rapid advancements, particularly in quantum teleportation and material simulation. Researchers have successfully demonstrated quantum teleportation through existing fiber optic networks, marking a significant leap from theoretical concepts to practical application. This allows information to be transferred instantly and securely by using quantum entanglement between particles without any physical movement of those particles. This achievement has been considered as a breakthrough and has been considered impossible prior to these findings.
The field of material simulation also shows huge improvements with a new quantum computing method that reduces computational resource requirements. This approach uses “pseudopotentials” to simplify interactions within atomic cores of materials, making simulations more practical and efficient. Quantum simulations were applied to study catalytic reactions, identifying over 3000 unique molecular configurations in the process. These advances demonstrate the growing importance of quantum mechanics in various areas of science, ranging from communication to material design, and also shows the potential for quantum advancements in many practical applications. Recommended read:
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@medium.com - 48d
Recent advancements in quantum computing highlight the critical mathematical foundations that underpin this emerging technology. Researchers are delving into the intricacies of quantum bits (qubits), exploring how they represent information, which is fundamentally different from classical bits, with techniques using packages like Qiskit. The mathematical framework describes qubits as existing in a superposition of states, a concept visualized through the Bloch sphere, and utilizes complex coefficients to represent the probabilities of measuring those states. Furthermore, the study of multi-qubit systems reveals phenomena such as entanglement, a critical resource that facilitates quantum computation and secure communication.
Quantum cryptography is another area benefiting from quantum mechanics, using superposition and entanglement for theoretically unbreakable security. Quantum random bit generation is also under development, with quantum systems producing truly random numbers critical for cryptography and simulations. In a different area of quantum development, a new protocol has been demonstrated on a 54-qubit system that generates long-range entanglement, highlighting the capabilities to control and manipulate quantum states in large systems, essential for scalable error-corrected quantum computing. These advancements are set against a backdrop of intensive research into mathematical models that represent how quantum phenomena differ from classical physics. Recommended read:
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@medium.com - 58d
The intersection of mathematics and technology is proving to be a hot topic, with articles exploring how mathematical concepts underpin many aspects of data science and programming. Key areas of focus include the essential math needed for programming, highlighting the importance of Boolean algebra, number systems, and linear algebra for creating efficient and complex code. Linear algebra, specifically the application of matrices, was noted as vital for data transformations, computer vision algorithms, and machine learning, enabling tasks such as vector operations, matrix transformations, and understanding data representation.
The relationship between data science and mathematics is described as complex but crucial, with mathematical tools being the foundation of data-driven decisions. Probability and statistics are also essential, acting as lenses to understand uncertainty and derive insights, covering descriptive statistics like mean, median, mode and the application of statistical models. Computer vision also relies on math concepts, with specific applications like optical character recognition using techniques like pattern recognition and deep learning. Optimization of computer vision models is also discussed, with a focus on making models smaller and faster using techniques like pruning and quantization. Recommended read:
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