Can anyone recommend exercise books for the following topic? I am applying for entrance exam to a few places in Taiwan and Japan for graduate studies in maths, statistics and data sciences, as their handling of a certain pandemic is decent and their tuition fee is amazing compared to the west.
Background: I did 5 semesters of analysis (parzynski, sherbert and bartle, rudin, spivak for Rn) in undergrad 1 semester of complex analysis (churchill ahlfors) in undergrad, 1 semester of Lebesgue integral (Royden). I have 0 knowledge of statistics and only basic probability up to joint distributions and basic combinatorics. I would be mostly concentrating on linear algebra, analysis, calculus, probability and statistics. Algebra and differential geometry I would leave it last. This is a link to their 2020 exam. https://www.i.u-tokyo.ac.jp/common/file/edu/course/mi/2020suuri-e.pdf
Calculus ( single -> multivariate) - includes series progressions and integrals, again some of their past year calculus has crazy sum of series ( did schaum's outline on calculus and advance calculus but then it doesn't seems enough, i need more practices for those series summation and multi integral. A link of their sample questions would be here ( https://mixedmoss.com/originmath/Emath.html) Please recommend exercise books on these.
Analysis ( Single, functional and complex) ( I did baby rudin but some questions in asian exams are non trivial) I would be working on rudin for analysis, erwin kreyzig for functional analysis, schaum outline for complex analysis ( some recommended ahlfors for the proofs, would it be enough? I think it is too much.)
Probability , Bayesian, Markov process, Markov Chains, Weak Lawe of large numbers and inequalities (doing sheldon ross a first course in probability) ( any recommendations? I need more practices for conditional probability, bayes theorem as i frequently misinterpret those difficult questions )
Algebra ( I am going through Gallian Contemporary Algebra and JB Fraleigh a first course in algebra, should i practice herstein topics in algebra?) (Would do dummit and foote when done)
Differential Geometry ( Is there a good introductory text with lots of examples and exercises on it? It doesnt come out often.)
Linear Algebra ( I am doing schaum's but it seems that it may not be enough especially for proving questions ) ( Linear algebra seems to be the most frequently tested but I have problems with summing of series of matrics and jordan canonical forms. Some of the proofs are non trivial too)
Statistics ( I am trying to go through introduction mathematical statistics by john rice and thereafter jun shao and casella and berger's mathematical statistics.) ( The recommendation is master the exercises in the 1st 10 chapters of casella for national taiwan university master's exam entrance exam)
Combinatorics ( they did have stirling number , PIE, derangement in some years) ( I am using schaum series too but it seems insufficient)