Resources
幾何研究的介紹性文章
Shapes of embedded minimal surfaces, Tobias H. Colding and William P. Minicozzi II, PNAS, 2006
〈數學傳播〉我在幾何分析的個人經驗,丘成桐,2018
〈數學傳播〉維騰形變及古典摩斯不等式的純解析證明,蕭欽玉,2017
Degenerations and moduli spaces in Kahler geometry,Song Sun,ICM 2018
Geometric Measure Theory - Recent Applications, Tatiana Toro, 2019
經典
數學普及文章
中小學數學互動學習網站
〈Mathigon〉
數學普及網站與刊物
〈UniMath〉
〈數學傳播〉
與物理、財務金融、其他科學相關
〈Quantamagazine〉Mathematicians Disprove Conjecture Made to Save Black Holes
〈科學Online〉初等的機率論(9)什麼是機率與機率法則?
〈綠角財經筆記〉債券的彎曲度
〈Kiss Science〉國科會做的科普網站
數據科學普及文章
〈CrossValidated〉Making sense of principal component analysis, eigenvectors & eigenvalues
〈玩具烏托邦〉資料科學/機器學習的好用入門工具 t-SNE 幫你看見高維度數值資料
〈寫點科普,請給指教。〉耗時三十年,深度學習之父HINTON是怎麼讓一度衰頹的類神經網路重迎曙光的呢?
〈DIGITIMES新聞〉卷積神經網路分析視網膜眼底成像 精準度可達99%
應用數學參考書
最佳化參考書
基本:Convex Optimization, Stephen Boyd and Lieven Vandenberghe
進階:Convex Optimization & Euclidean Distance Geometry, Jon Dattorro
有限維變分:Variational Analysis, Rockafellar and Wets
無窮維變分:Variational Analysis and Generalized Differentiation, I & II, Mordukhovich
其他變分:Techniques of Variational Analysis, Borwein and Zhu
數據科學參考書
大學生最佳入門書:Mathematical Foundations of Big Data Analytics, Vladimir Shikhman and David Müller
只要會基礎大學數學就可以讀懂,涵蓋主題夠多,從具體應用實例來介紹背後的數學。取材很好(但我沒仔細看證明的推導,有機會再說)。Geometric Structure of High-Dimensional Data and Dimensionality Reduction, Jianzhong Wang
Foundations of Data Science, Avrim Blum, John Hopcroft, and Ravindran Kannan
深度夠,偏應用的角度來寫,有些數學只有陳述,沒詳細解釋。MDS
Modern Multidimensional Scaling: Theory and Applications (Springer Series in Statistics), Ingwer Borg and Patrick J. F. Groenen
Some distance properties of latent root and vector methods used in multivariate analysis, J. C. Gower, 1966
Metric and Euclidean Properties of Dissimilarity Coefficients, J. C. Gower and P. Legendre, 1986