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A-Maths@Maths on Medium - 60d
A series of Medium articles offer accessible explanations of diverse mathematical concepts and their real-world applications. Topics covered include solving various types of equations, from basic algebraic problems to more advanced exponential equations relevant to data science. One article provides a step-by-step guide to understanding and solving equations, emphasizing the importance of this skill across numerous fields like finance and programming. Another article tackles the frequency illusion, also known as the Baader-Meinhof phenomenon, explaining the cognitive bias behind why we notice things more frequently after becoming newly aware of them.
Furthermore, the collection explores the significant relationship between mathematics and coding, illustrating how mathematical principles underpin fundamental concepts in computer science such as algorithms, data structures, and computational complexity. The articles also include practical applications, like using exponential equations in data science and demonstrating the use of linear regression in predictive analytics. A selection of math puzzles with answers is also provided, offering engaging challenges for readers to test and hone their problem-solving skills. Recommended read:
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@medium.com - 55d
Recent articles and blog posts have highlighted key machine learning concepts and their applications, focusing particularly on the role of probability and statistics. These foundational mathematical tools are essential for understanding how machine learning models make decisions. Key areas explored include probability distributions like uniform, normal, Bernoulli, binomial, and Poisson, each with specific applications in model training and data analysis. Furthermore, the concept of conditional probability is discussed, explaining how the likelihood of an event changes based on other events, using real-world examples. Understanding of these concepts is fundamental for building effective ML models.
The importance of data sampling in machine learning has also been addressed, emphasizing how crucial representative data sets are to achieving accurate predictions. Techniques such as random sampling and stratified sampling ensure models can generalize well to new data, addressing potential biases caused by class imbalances through over-sampling or under-sampling techniques. Articles also showcase how techniques like decision trees and random forests are being applied for tasks such as customer churn prediction, and the use of matrices and GPUs for accelerating deep learning computations. The interrelationship between math and coding is highlighted, noting the significance of mathematical principles in algorithms, data structures, and computational complexity. Recommended read:
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@medium.com - 18d
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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@www.primaryresources.co.uk - 17d
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Pat'sBlog
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Recent discussions have focused on the fundamentals of subtraction in mathematics education, exploring its historical roots and teaching methods. The operation of finding the difference between two numbers is called subtraction, with terms like ‘minus,’ ‘less,’ and ‘decrease’ being used. The symbol "-" was originally used in Germany to indicate underfilled barrels and later became an operational symbol in the 1500's. Early texts often used "subduction" to describe subtraction before settling on "subtraction".
The concept of 'borrowing,' also known as 'regrouping,' in subtraction has been analyzed with varying perspectives through history. Some educators prefer the term 'regrouping,' over 'borrowing' to emphasize the concept of understanding the process rather than viewing it as a rote procedure. There is reference in older works to the method of subtraction, now commonly known as borrowing, being taught in the 1200's. Subtraction with small numbers can be computed horizontally, while larger numbers are handled vertically by using place value charts. A number subtracted from itself yields zero, and subtracting zero from a number doesn’t change that number's value. Recommended read:
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@vatsalkumar.medium.com - 13d
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medium.com
Recent articles have focused on the practical applications of random variables in both statistics and machine learning. One key area of interest is the use of continuous random variables, which unlike discrete variables can take on any value within a specified interval. These variables are essential when measuring things like time, height, or weight, where values exist on a continuous spectrum, rather than being limited to distinct, countable values. The concept of the probability density function (PDF) helps us to understand the relative likelihood of a variable taking on a particular value within its range.
Another significant tool being explored is the binomial distribution, which can be applied using programs like Microsoft Excel to predict sales success. This distribution is suited to situations where each trial has only two outcomes – success or failure, like a sales call resulting in a deal or not. Using Excel, one can calculate the probability of various sales outcomes based on factors like the number of calls made and the historical success rate, aiding in setting achievable sales goals and comparing performance over time. Also, the differentiation between binomial and poisson distribution is critical for correct data modelling, with binomial experiments requiring fixed number of trials and two outcomes, unlike poisson. Finally, in the world of random variables, a sequence of them conditionally converging to a constant value has been discussed, highlighting that if the sequence converges, knowing it passes through some point doesn't change the final outcome. Recommended read:
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@medium.com - 29d
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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@tracyrenee61.medium.com - 33d
Recent discussions have highlighted the importance of several key concepts in probability and statistics, crucial for data science and research. Descriptive measures of association, statistical tools used to quantify the strength and direction of relationships between variables are essential for understanding how changes in one variable impact others. Common measures include Pearson’s correlation coefficient and Chi-squared tests, allowing for the identification of associations between different datasets. This understanding helps in making informed decisions by analyzing the connection between different factors.
Additionally, hypothesis testing, a critical process used to make data-driven decisions, was explored. It determines if observations from data occur by chance or if there is a significant reason. Hypothesis testing involves setting a null hypothesis and an alternative hypothesis then the use of the P-value to measure the evidence for rejecting the null hypothesis. Furthermore, Monte Carlo simulations were presented as a valuable tool for estimating probabilities in scenarios where analytical solutions are complex, such as determining the probability of medians in random number sets. These methods are indispensable for anyone who works with data and needs to make inferences and predictions. Recommended read:
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@gregrobison.medium.com - 46d
Recent articles are exploring the practical applications of mathematics across various fields and skill levels. One focus is on linear regression, with detailed guides covering the theory, implementation from scratch using tools like NumPy, and even a demonstration of a needlessly complicated tool for the same purpose. These resources are aimed at helping people understand the math behind machine learning algorithms and their real-world applications, such as predicting housing prices, forecasting sales, and analyzing scientific data.
The use of Large Language Models (LLMs) in mathematics education is another key area of investigation. While LLMs demonstrate remarkable capabilities in language generation, they struggle with direct mathematical problem-solving, instead they use coding to indirectly solve mathematical problems. However, they can be powerful tools for helping students, for instance, ChatGPT can be used to solve math problems with step-by-step instructions and can also read research papers and provide explanations. Additionally, topics like multinomial distributions, and real world mathematical analysis from The Cat In The Hat are being explored to further enhance mathematical understanding. Recommended read:
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@medium.com - 45d
Cryptography is the cornerstone of secure digital communication, utilizing mathematical algorithms to protect information and ensure privacy. It involves transforming data into an unreadable format only authorized parties can understand. There are two main types of cryptography: symmetric and asymmetric. Symmetric cryptography uses the same key for both encryption and decryption, making it fast and efficient for large volumes of data, however, key distribution can be challenging. Examples include AES and DES.
Asymmetric cryptography, or public-key cryptography, uses a pair of keys; a public key for encryption and a private key for decryption. It provides secure key distribution and enables digital signatures but is slower and requires more computational resources than symmetric methods. RSA and ECC are examples of this. These methods are used in SSL/TLS protocols to secure internet communications, ensuring data transmission is protected through processes like handshakes, which establish shared keys. Additionally, cryptography is critical for blockchain technology, utilizing hashing to ensure data integrity and employing digital signatures for secure transactions. Recommended read:
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