Math

Writing Mathematical Equations in Markdown Tex Format Setting up partials We will use the functionality of partial templates. https://gohugo.io/templates/partials/ Create a folder named partials under the layouts directory. \layouts\partials Place two files in this directory. mathjax.html <script type="text/javascript" async src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/MathJax.js?config=TeX-MML-AM_CHTML"> </script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ tex2jax: { inlineMath: [['$', '$'] ], displayMath: [ ['$$','$$'], ["\\[","\\]"] ] } }); </script> footer.html <footer> {{ partial "mathjax.html" . }} </footer> Example of Mathematical Equations Simply surround the tex notation with $. Formula for solving quadratic equations $ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $ ...

Overview 📝 This article explores the Softmax function, a crucial component in machine learning. The Softmax function transforms arbitrary real-valued vectors into probability distributions, making it essential for multi-class classification problems. We’ll dive into its fundamental mechanisms, mathematical definition, key properties, and practical applications. Demystifying the Softmax Function 🧮 The softmax function is a crucial tool in machine learning, particularly for multi-class classification problems. Essentially, it takes a vector of arbitrary real numbers (positive, negative, zero, etc.) and transforms it into a probability distribution. This means the output is a vector of values between 0 and 1 that add up to 1, representing the probability of each class. ...

📊 Understanding Odds Ratio and Risk Ratio 🎯 What is Risk Ratio? Risk Ratio is a measure that represents the ratio of risks (incidence rates) between two groups. Let’s explain using hypothetical data: COVID-19 Positive COVID-19 Negative Total Incidence Rate Not Wearing Mask 90 10 100 Pa = 90% Wearing Mask 40 160 200 Pb = 20% 💡 Calculating Risk Ratio Risk Ratio is calculated using the following formula: ...

一般向けIUT・abc予想について。 IUT・abc予想 足し算と掛け算に関わる関係を明らかにする理論と言われます。 また、強いabc予想のもとでは、フェルマーの最終定理が背理法により簡単に導出されます。 ABC予想のよくある間違い https://tsujimotter.hatenablog.com/entry/misunderstanding-of-abc-conjecture ブログ/Web 新一の「心の一票」 - 楽天ブログ https://plaza.rakuten.co.jp/shinichi0329/ 宇宙際タイヒュミラ−理論への誘（いざな）い http://www.kurims.kyoto-u.ac.jp/~motizuki/Uchuusai%20Taihimyuuraa%20riron%20he%20no%20izanai%20(lecture%20note%20ban).pdf 参考書籍 宇宙と宇宙をつなぐ数学　IUT理論の衝撃 (角川学芸出版単行本) https://www.amazon.co.jp/dp/B07QVHZJL8/ref=cm_sw_em_r_mt_dp_P0WNTWA4ZG3RZJ4SE7JB 参考動画 IUT abc Conjecture and New Mathematics - Prof. Fumiharu Kato, Oct 7, 2017 (with English subtitles) abc予想の主張を理解する