Shenduo's Homepage

Homework

Here are some of my homework done in class. Those contents are chronically ordered. Many of my undergraduate homeworks are in Chinese, particularly group projects. But those written individually by myself are usually in English. Those homeworks’ quality are not very stable, depending on my time and attention dedicated to the course.

All homework demonstrated here were finished by myself and myself only if not specified. I’m fully responsible for the commitment to honesty, independence and reproducibility of all those. Although careless typos and stupid mistakes can be found easily in my homework, violation of academic principles has never been in them, and they will never be.

I’m not responsible for any outcomes for usage of those contents, be aware and expected to find mistakes in those contents.

If you have any questions about the materials or found any errors, feel free to contact me through email, which you can find at the bottom of this webpage.

2020 Fall

Functional analysis

  • Lecturer: Jiaqing Yang
  • Institute: Xi’an Jiaotong University
  • Grade: Not available yet

  • English

  • Metric space and convergence. pdf
  • Completeness, compactness and Sobolev embeddings. pdf
  • Banach's theorem and Fredholm equation. pdf
  • projections, Banach space and Poincare inequalities. pdf
  • Inner product space, Hilber space and Orthogonal decomposition. pdf
  • Basis and Operator norm. pdf
  • Hahn-Banach theorem, Riesz representation theorem and Lax-Milgram theorem. pdf
  • Geometric form of Hahn-Banach theorem. pdf
  • Dual Space and Adjoint Operator. pdf
  • Weak convergence pdf
  • We also had some homework on the spectrum of linear operators and Fredholm operators related, but I didn’t wrote latex for that.

Statistical consultary

  • Lecturer: Xuehu Zhu
  • Institute: Xi’an Jiaotong University
  • Reference book: Lecture notes
  • Grade: Not available yet

The reports are all in Chinese and the code written are basically without much comments. But by running the code, you do reproduce what we did.

  • Homework on generalized linear model and asymptotic normality for parameter estimation in parameterized non-linear model. Collaborated with Shaokang Zu.
    • Report pdf
    • R code, R studio project and RMD notebook code
  • Homework on principle component analysis and factor model. Collaborated with Shaokang Zu.
    • Report pdf
    • R code, R studio project and RMD notebook code
  • Homework on non-parametric density estimation and non-parametric regression. Collaborated with Shaokang Zu.
    • Report pdf
    • R code, R studio project and RMD notebook code
  • Final report on optimality.

Big data analysis

  • Lecturer: Junmin Liu, Qian Zhao
  • Institute: Xi’an Jiaotong University
  • Reference book: Lecture notes

  • Grade: Not available yet

  • Final report on Spectral Net(Joint with Zehao Wang, Chenghang Wang and Yufei Yan). pdf

High-dimensional inference

  • Lecturer: Xuehu Zhu
  • Institute: Xi’an Jiaotong University
  • Reference book: Lecture notes
  • Grade: Not available yet

2020 Spring

Machine learning

  • Lecturer: Deyu Meng
  • Institute: Xi’an Jiaotong University
  • Reference book: Lecture notes
  • Grade: 93/4/A

These works were jointly done in a group of three with Zehao Wang and Chenghang Wang. We had a good time together and personally I appreciate this pleasant collaboration experience. Collaborators: Zehao Wang, Chenghang Wang

  • Overview of ML and different approach comparing to statistics. pdf
  • SEIR model on pandemic modelling. pdf
  • CNN, transfer learning and visualization for training of convolution layers and extracted features. pdf
  • Boosting and SVM. pdf
  • Unsupervised learning, k-means, fuzzy c-means and kernel fuzzy c-means. pdf
  • Visualization of GAN training. pdf

Data analysis and R(Chinese)

  • Lecturer: Chunxia Zhang
  • Institute: Xi’an Jiaotong University
  • Grade: 97/A/4.0
  • Chinese

Reports are in Chinese because it was required.

  • basic sample statistics. pdf
  • linear regression. pdf
  • ANOVA and statistical inference. pdf
  • PCA and Canonical analysis. pdf
  • Classification analysis, including LDA. pdf

Elements of biological statistics

  • Lecturer: Hongying Zhang
  • Institute: Xi’an Jiaotong University
  • Grade: 92/A/4.0

  • English

  • Basic visualization. pdf
  • EM algorithm. pdf
  • Chi-sqaure independence test, McNemar test (exact and normal) and Fisher exact test with biological data. pdf
  • Wilcoxon signed rank test (normal and exact) and Wilcoxon rank-sum test (normal and exact) with biological data. pdf
  • Random and fixed effect ANOVA with biological data. pdf

Optimization(Chinese)

  • Lecturer: Hui Li
  • Institute: Xi’an Jiaotong University
  • Grade: 89/A-/3.7
  • Chinese

This homework set contains many handwritten ones. I do not enjoy any reputation of good calligraphy, so be prepared while you read them.

  • convexity, descend direction and optimality. pdf
  • Linear programming and simplex. pdf
  • Linear search, Goldstein and Wolfe principle and speedy descend. pdf
  • Non-restricted optimization. pdf
  • Quadratic programming. pdf
  • Linear search.

2019 Fall

Mathematical statistics

  • Lecturer: Mayya Zhilova
  • Institute: Georgia Institute of Technology
  • Grade: A/4.0
  • English

Somehow there was only one homework for this class.

Stochastic processes

  • Lecturer: Lutz Warnke
  • Institute: Georgia Institute of Technology
  • Grade: A/4.0
  • English

2017 Fall-2019 Spring

Only the following homeworks are available

  • Mathematical analysis (first semester out of three)
  • Advanced algebra (first semester out of two)

I was using electronic homeworks at first. However, I switched back to hand-written ones after the first semester. Those early contents are hand-written in Chinese, parts of them are here OneNote.

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