Machine learning的数学基础:
Linear Algebra:跟完MIT OCW Pro. Strang的 Linear Algebra and its Applications
Statistics: 国内教材的话陈希孺先生的《概率论与数理统计》一书吃透学习一般的ML算法已足够,深入可参考Berger的Statistical Inference
Optimization:Stanford的Boyd开的Convex Optimization课程及他本人写的教材,另参考Numerical Optimization一书
Machine Learning书籍:
Frequentist观点:The Elements of Statistical Learning
Bayesian观点:Pattern Recognition and Machine Learning
难度更大更全面的:Machine Learning: A probablistic perspective, 基本已经跟进到当下学届最前沿的内容了, e.g. Deep Learning