Recommended Reading
Hello everyone. My name is Tokuda, and I lead the Neurodynamics Laboratory at the Faculty of Health Data Science, Juntendo University.
Recently, I have been receiving many questions such as:
“What should I study before joining the laboratory? Are there any books I should read beforehand?”
So, I decided to list some books here that I can recommend.
The kinds of knowledge used in our laboratory include the following:
- Linear Algebra
- Multivariable Calculus
- Dynamical Systems
- Information Theory
- Fourier Analysis
- Machine Learning
- Computational Neuroscience
- Basics in Neuroscience
If I were to select only a few books that are particularly worth reading before entering graduate school,
for dynamical systems I would recommend:
Differential Equations, Dynamical Systems, and an Introduction to Chaos
(Morris W. Hirsch, Stephen Smale, Robert L. Devaney),
or
Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering
(Steven H. Strogatz).
For neuroscience:
Principles of Neural Science (Eric Kandel et al.),
and 『脳の計算論（甘利俊一監修）』.
For machine learning:
The Elements of Statistical Learning (Hastie, Tibshirani, Friedman).
If you are not yet comfortable with linear algebra or multivariable calculus, please start by studying those areas thoroughly. Concepts such as matrix rank, determinants, eigenvalues and eigenvectors, coordinate transformations, Taylor expansions, line integrals, derivatives along curves, gradients, Jacobians, and Fourier transforms will be considered prerequisites.
Dynamical Systems
- Differential Equations, Dynamical Systems, and an Introduction to Chaos — Morris W. Hirsch, Stephen Smale, Robert L. Devaney (2012)
- Nonlinear Dynamics and Chaos — Steven H. Strogatz (2015)
- 合原一幸『カオス学入門（放送大学教材）』
- 郡宏『生物リズムと力学系』
- Edward Ott “Chaos in Dynamical Systems”
Neuroscience
- Principles of Neural Science, Fifth Edition — Eric Kandel et al. (2012)
- Neuroscience: Exploring the Brain — Mark Bear, Barry Connors, Michael A. Paradiso (2025)
- Physiology of Behavior, Global Edition (13th Edition) — Neil Carlson, Melissa Birkett
- 甘利俊一監修『脳の計算論（シリーズ脳科学 1）』
- 『脳単』
- 『NEW薬理学』
- E. M. Izhikevich “Dynamical Systems in Neuroscience”
- 川人光男『脳の計算理論』
Machine Learning
- The Elements of Statistical Learning — Hastie, Tibshirani, Friedman
- Pattern Recognition and Machine Learning — Christopher M. Bishop
Other Mathematics & Physics
- 今井秀樹『情報理論』
- 日野幹雄『スペクトル解析』
- 田崎晴明『統計力学』
- 清水明『熱力学の基礎』
- 清水明『量子論の基礎』
- 小出昭一郎『量子力学』
- 松本和夫『多様体の基礎』
- 齋藤正彦『数学の基礎—集合・数・位相』
- 志賀浩二『30講シリーズ』
General Reading
- Phantoms in the Brain — V. S. Ramachandran, Sandra Blakeslee
- Vision: A Computational Investigation into the Human Representation and Processing of Visual Information — David Marr
- Descartes' Error — Antonio Damasio
- The Quest for Consciousness — Christof Koch
- The Science of Structure: Synergetics — Hermann Haken
- Pioneers of Celestial Mechanics
- 『脳科学のテーブル』
- 津田一郎『カオス的脳観』『ダイナミックな脳』
- 木村敏『心の病理を考える』
- 清水博『生命を捉えなおす』
- 多賀源太郎『脳と身体の動的デザイン』
- 蔵本由紀『非線形科学』
- 大野『非線形な世界』
- チョムスキー『生成文法の企て』
- 佐々木正人『アフォーダンス』
- 佐藤文隆『破られた対称性』
Some well-known models used in computational neuroscience include:
- Hodgkin–Huxley model
- Hopfield model
- Boltzmann machine
- Perceptron
- FitzHugh–Nagumo model
- Integrate-and-fire neuron model
- Chaotic neural networks
- Kuramoto model
- Chaotic itinerancy
- Marr’s three levels
These are examples of foundational models. There may not be a single book that covers all of them comprehensively, but it is useful to be familiar with the basic ideas behind each.