Contents

General Information

References

  • J. W. E. Boyce and R. C. DiPrima, Elementary differential equations and boundary value problems, John Wiley and Sons, Inc., Hoboken, NJ, 12th edition, 2022. MR0179403, Zbl:1492.34001
  • P.-F. Hsieh and Y. Sibuya, Basic theory of ordinary differential equations, Universitext, Springer-Verlag, New York, 1999. MR1697415, doi:10.1007/978-1-4612-1506-6

Prerequisite

  • Real and complex analysis

Homeworks

  • Homework 1: Return by September 26, 2024 (Thursday) 23:59
  • Homework 2: Return by October 10, 2024 (Thursday) 23:59
  • Homework 3: Return by October 31, 2024 (Thursday) 23:59
  • Homework 4: Return by November 7, 2024 (Thursday) 23:59
  • Homework 5: Return by December 12, 2024 (Thursday) 23:59

Schedule

  • The lectures are on Thursday (13:10-16:00) at 志希070116.
Time Room Activities
12.09.2024 13:10-16:00 志希070116 Week 1 - Lecture (Thursday): Well-posedness of ODE
19.09.2024 13:10-16:00 志希070116 Week 2 - No class
26.09.2024 13:10-16:00 志希070116 Week 3 - Lecture (Thursday): First order linear PDE [Return Homework 1 by September 26, 2024 (Thursday) 23:59]
3.10.2024 13:10-16:00 志希070116 Week 4 - No class due to Typhoon Krathon
10.10.2024 13:10-16:00 志希070116 Week 5 - No class (Public holiday) [Return Homework 2 by October 10, 2024 (Thursday) 23:59]
17.10.2024 13:10-16:00 志希070116 Week 6 - Lecture (Thursday): First order quasilinear PDE, homogeneous linear ODE with constant coefficients
24.10.2024 13:10-16:00 志希070116 Week 7 - Lecture (Thursday): Computations of the exponential, the matrix logarithm
31.10.2024 13:10-16:00 志希070116 Week 8 - No class due to Typhoon Kong-rey [Return Homework 3 by October 31, 2024 (Thursday) 23:59]
7.11.2024 13:10-16:00 志希070116 Week 9 - Lecture (Thursday): matrix Lie group and Lie algebra [Return Homework 4 by November 7, 2024 (Thursday) 23:59]
click me to see the title and abstract of today's first talk (50 minutes)
Speaker. Lin, Po-Yi
Title. Theory of Transformer
Abstract. The dominant sequence transduction models are based on complex recurrent or convolutional neural networks that include an encoder and a decoder. The best performing models also connect the encoder and decoder through an attention mechanism. We propose a new simple network architecture, the Transformer, based solely on attention mechanisms, dispensing with recurrence and convolutions entirely. Experiments on two machine translation tasks show these models to be superior in quality while being more parallelizable and requiring significantly less time to train. Our model achieves 28.4 BLEU on the WMT 2014 English-to-German translation task, improving over the existing best results, including ensembles, by over 2 BLEU. On the WMT 2014 English-to-French translation task, our model establishes a new single-model state-of-the-art BLEU score of 41.0 after training for 3.5 days on eight GPUs, a small fraction of the training costs of the best models from the literature.
14.11.2024 13:10-16:00 志希070116 Week 10 - Lecture (Thursday): Homogeneous ODE with variable coefficients
click me to see the title and abstract of today's first talk (50 minutes)
Speaker. Cheng, Huan-Chang
Title. An introduction to the Simplex Method
Abstract. Linear programming problems are applied in many fields, such as finance, transportation, management, and agriculture. In this talk, we will provide a brief overview of some linear programming theories and explain the design principles of the simplex method, an algorithm used to solve linear programming problems.
21.11.2024 13:10-16:00 志希070116 Week 11 - Lecture (Thursday): nonhomogeneous equations, higher order linear ODE
28.11.2024 13:10-16:00 志希070116 Week 12 - Lecture (Thursday)
5.12.2024 13:10-16:00 志希070116 Week 13 - Lecture (Thursday)
click me to see the title and abstract of today's first talk (50 minutes)
Speaker. Fan, Min-Yuan
Title. An introduction to divergence and curl
Abstract. We will introduce the definitions of divergence and curl and discuss their physical significance and some properties.

click me to see the title and abstract of today's second talk (50 minutes)
Speaker. Chang,Wen-Ling
Title. An introduction to Natural Language Processing (NLP) and its application - Use AI to continue writing the Dream of the Red Chamber (紅樓夢)
Abstract. We will introduce the main concept of the NLP, its key technology and an application to the literature "Dream of the Red Chamber" via the Natural Language Understanding (NLU) and the Natural Language Generator (NLG) technology. We will exhibit how the AI learn the literary style of the literature and extend it by using the NLP technology.

click me to see the title and abstract of today's third talk (50 minutes)
Speaker. Ｗu, Ju-Yen
Title. An introduction to the Monte Carlo method and its applications
Abstract. Monte Carlo method is a numerical computation approach based on probability and statistics, through random number generation to solve complex problems. In this talk, we will explore the core principles of this method, its advantages and limitations, as well as its extended algorithms and applications.
12.12.2024 13:10-16:00 志希070116 Week 14 - No class [Return Homework 5 by December 12, 2024 (Thursday) 23:59]
19.12.2024 13:10-16:00 志希070116 Week 15 - Lecture (Thursday)
click me to see the title and abstract of today's first talk (50 minutes)
Speaker. Chang,Wen-Ling
Title. An introduction to the Kalman Filter
Abstract. Kalman Filter is an algorithm based on linear algebra and probability, which is widely used to approximate the "status" of dynamical systems. It gives the best approximation (and reduce noises) for the "status" based on data from sensors and mathematical models. We will introduce the mathematical principle and model of the Kalman Filter from the probability point of view and explain its applications.

Completion

  • The course can be taken for credit by attending the lectures, returning written solutions (60%) in LaTeX and giving (at least) 2 presentations (each 20%).