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Ada Lovelace: The World’s First Computer Programmer

為了解決Mathematician的問題，作者Cox, Annabelle 這樣論述：

While much has been written about the 'father of computers' Charles Babbage and Alan Turing, the pioneer of computer science, many trailblazing female computer programmers have slipped beneath the radar. One of these is Ada Lovelace. A Countess and daughter of the infamous Lord Byron, Lovelace co

uld have lived a very comfortable if unremarkable life, but instead she became a renowned mathematician and writer. She is chiefly known for her work with Charles Babbage, the aforementioned 'father of computers'. But it was actually Ada and not Babbage who was the first person to recognize that the

machine had applications beyond pure calculation. She created the first algorithm intended to be carried out by such a machine and, as a result, she is regarded as the world's very first computer programmer. Her life is fascinating, taking in social and educational exploits with the leading scienti

sts and writers of her day, including Charles Dickens. This new biography seeks to acquaint the reader with all the various milestones of an inspiring life and career.Ada Lovelace is increasingly becoming recognized as a true icon for women in technology. With girls and young women being encouraged

ever more into the fields of mathematics, technology and science (fields previously dominated by men), women such as Ada are incredibly powerful figureheads with influential legacies. Her story is an inspiration to anyone seeking to break new ground in their chosen field.

Mathematician進入發燒排行的影片

數學形態學導出多參數持續同調之層狀結構

為了解決Mathematician的問題，作者胡全燊 這樣論述：

Topological Data Analysis (TDA), a fast-growing research topic in applied topology, uses techniques in algebraic topology to capture features from data. Its importance has been discovered in many areas, such as medical image processing, molecular biology, machine learning, and pattern recognition.

Persistent homology (PH) is vital in topological data analysis that detects local changes in filtered topological spaces. It measures the robustness and significance of homological objects in spaces' deformation, such as connected components, loops, or higher dimensional voids. In Morse theory, filt

ered spaces for persistent homology usually rely on a single parameter, such as the sublevel set filtration of height functions. Recently, as a generalization of persistent homology, computational topologists began to be interested in multi-parameter persistent homology. Multi-parameter persistent h

omology (or multi-parameter persistence) is an algebraic structure established on a multi-parametrized network of topological spaces and has more fruitful geometric information than persistent homology. So far, finding methods to extract features in multi-parameter persistence is still an open and

concentrating topic in TDA. Also, examples of multi-parameter filtration are still rare and limited. The three principal contributions of this dissertation are as follows. First, we combined persistent homology features (persistence statistics and persistence curves) and machine learning models for

analyzing medical images. We found that adding topological information into machine learning models can improve recognition accuracy and stability. Second, unlike traditional construction for multi-parameter filtrations in Euclidean spaces, we propose a framework for constructing multi-parameter fi

ltrations from digital images through mathematical morphology and discrete geometry. Multi-parameter persistence derived from mathematical morphology is more efficient for computing and contains intuitive geometric attributes of objects, such as the sizes or robustness of local objects in digital im

ages. We involve these features to remove the salt and pepper noise in digital images as an application. Compared with current denoise algorithms, the proposed approach has a more stable accuracy and keeps the topological structures of original data. The third part of this dissertation focuses on us

ing sheaf theory to analyze the lifespans of objects in multi-parameter persistence. The multi-parameter persistence has a natural sheaf structure by equipping the Alexandrov topology on the based partially ordered set. This sheaf structure uncovers the gluing properties of local image regions in th

e multi-parameter filtration. We referred to these properties as a fingerprint of the filtration and applied them for the character recognition task. Finally, we propose using sheaf operators to define ultrametric norms on local spaces in multi-parameter persistence. Like persistence barcodes, this

metric provides finer geometric and topological quantities.

Regression, a Friendly Guide

為了解決Mathematician的問題，作者Rudd, Matthew 這樣論述：

Matthew Rudd is a mathematician fascinated by statistical modeling, data analysis, and the tensions between theory, practice, and interpretability in data science. He teaches mathematics and statistics at Sewanee (The University of the South), a liberal arts college in Tennessee.

古中國水力機械天文鐘系統化復原設計

為了解決Mathematician的問題，作者黃正輝 這樣論述：

目錄Contents中文摘要………………………………………………………………..ΙAbstract (in Chinese)英文摘要……………………………………………………………….ⅡAbstract (in English)誌 謝..………………………………………………………………ⅤAcknowledgments目錄………………………………………………………….…………ⅥContents圖目錄…………………………………………………………………...ⅩList of Figures表目錄………………………………………………………...….ⅩVList of Tables第一章 介紹……………

……………………………………………….1Introduction1-1 文獻探討與分析………………………………………….…...1Literature Review and Analysis1-2 研究動機……………………………………………………..12Research Motivation.1-3 研究目的……………………………………………………..13Research Objectives1-4 論文架構………………………………………………….…..15Dissertation Structure第二章 古中國天文學的研究……………………………………..….17On the Histori

cal Development of theAstronomical Clocks in ancient China2-1 天象觀測………………………………………………….….17Astronomical Observation2-2 天文觀測儀器的發展演進…………………………………..20The Evolution of Astronomical Observing Instrumentscation Lists2-3 時間制度……………………………………………………...32Time Law.2-4 結論..……………………………………………………..…...33Summary第三章 水力

機械鐘的歷史發展……………………………..………34On the Historical Development for Hydro-MechanicalClocks3-1 漏壺的形制與途……………………………...…………........35Types and Uses of Clepsydras3-2 控制系統的發展………………………………...………........38The Developments of Control System3-3 動力傳動系統………………………………………………...41Powered-transmission Systems3-4 顯時與報時置…………………

………………………..…….46Time Indicator and Reporting Devices3-5 結論……………………………………………..………..…...51Summary第四章 水力機械鐘的作動研究………..……………...………...…..52Study on Operation Models for Hydro-Mechanical Clocks4-1 古代水力機械鐘運動模式研究……...………...………...…..52Study on the Kinematic Models for the Water-PoweredMechanical Clocks in Anc

ient Time4-2 水力機械鐘作動流程…………………………………...…....63Study on the Kinematic Model of Hydro-Mechanical Clocks4-3 結論………………………………………………….……......75Summary第五章 古中國機械天文鐘的復原方法………………………...…...76The Reconstruction Designs Approach for AncientChinese Astronomical Mechanical Clocks5-1 古機械復原序……………………………………………..….76Proc

edure of the Reconstruction Designs for AncientMachinery5-2 模型設計與製造……………………………………………..78Design and Manufacture of the Reconstruction Models5-3 結論………………………………………………….……….79Summary第六章 復原設計實例……………………………………………......80Examples of the Reconstruction Design6-1 Examp1eⅠ：東漢張衡水運渾象復原……………..………….80Eastern Han D

ynasty Zheng Heng’s WatertransportCelestial Globe Reconstruction Design6-2 Examp1eⅡ：唐朝僧一行與梁令瓚水運天復原…………....106Tan Dynasty Yi Xing and Liang Ling-Zan’s WatertransportCelestial Sphere Reconstruction Design6-3 Examp1eⅢ：北宋張思訓太平渾儀復原…………………...131Northern Song Dynasty Zheng Si-Xun’s Tai PingHun Yi Reconstuc

tion Design6-4 結論………………………………………………..………...160Summary第七章 結論與展望…………………………………………….…...161Conclusions and Prospects7-1 結論…………………………………………………………161Conclusions7-2 展望………………………………………………………....162Prospects參考文獻……………………………………………………...…….....164References著作權聲明……………………………………………………..........173Copyright Statemen

t附錄 發表論文………………………………………………..........174Appendix Publication Lists