CS 592: Automated Reasoning and Machine Learning Integration

Course Information

When: 11:30 am -- 12:20 pm, Mon/Wed/Fri.

Where: LSWN B134.

Instructor: Yexiang Xue, yexiang@purdue.edu.

Office Hour: ??? Appointments need to be filed (via emails) at least 24 hours in prior.

Course website: https://www.cs.purdue.edu/homes/yexiang/courses/26spring-cs592/index.html.

Notifications and slides will be via Brightspace (https://purdue.brightspace.com/).

Discussions will be via emails, office hours, (virtual) meetings.

Course project submission at Gradescope.

Course Description

Automatic reasoning and machine learning are two fundamental pillars of Artificial Intelligence (AI). Reasoning includes SATisfiability (SAT) solving, constraint programming, and probabilistic inference. The development of automated reasoning was motivated by symbolism, one school of thought within AI that believes that human-level intelligence can be achieved via logical or numerical symbolic reasoning. Learning, as the other major branch of AI, contains probabilistic modeling, structured prediction, and neural generation. The development of machine learning was heavily influenced by connectionism, which believes that intelligence emerges from complex connections, for example, the one that connects billions of synapses in a human brain. Connectionism seeded the development of artificial neural networks as we know today. Historically, reasoning and learning each led the charge of AI development in different times. For example, expert systems, the signature product of the second AI summer in the 1980s, were entirely reasoning-based. The now popular large language models, on the other hand, are learning-based.

Nevertheless, fundamental difficulties are present when reasoning or learning are applied in isolation. Reasoning without learning leads to rigid and brittle formulations, while learning without reasoning produces suboptimal models violating critical constraints, hallucinating, and behaving unexpectedly in unseen situations. The integration of learning and reasoning is of pivotal importance. In fact, the lack of reasoning capabilities is agreed among leading AI scientists to be a major limitation of current foundational models ("The amount of reasoning happening in Large Language Models (LLMs) is very very primitive..." -- Yann LeCun (Turing award winner for creating deep learning) answering "Can LLMs reason?")

This course explores how the integration of automated reasoning and machine learning will unleash the potentials of next generational AI. We will start from discussing a few successful cases of reasoning and learning integration. This includes:

• Integrating reasoning for learning and decision-making with optimality guarantees: Guarantees are crucial for many real-world problems. For example, can my road network design guarantee multiple safe evacuation routes when a natural disaster hits? Is my learned model the best fit to the training data? Answering these questions requires mixed symbolic and statistical inference with provable guarantees. This course will introduce a new formal language, Satisfiability Modulo Counting (SMC) to unify these two types of inference. We will discuss a novel algorithmic idea harnessing hashing and randomization, which is able to attain double-sided, constant approximation guarantee for solving SMC. We also will discuss how this idea transforms learning of energy-based models, solving leader-follower games, and planning under uncertainty.
• Integrating reasoning for learning with constraint satisfaction: The lack of constraint satisfaction guarantees remains a critical limitation of neural networks, especially in safety-related domains. In this class, we will discuss recent approaches which augment neural networks with fully differentiable constraint reasoning layers to ensure constraint satisfaction. We will demonstrate the paradigm shifts this approach has brought in constrained natural language generation, data-driven operational research, robotic surgery, and neural image generation.
• Integrating reasoning to speed up learning, focusing on expediting scientific discovery using AI: We will discuss how the integration of scientific reasoning speed up neural learning models in finding fundamental physics laws from experiment data. Also, we will talk about how the reasoning integrated learning approaches led to advancement real scientific discoveries in several domains.

The goal of this course has two folds. First, this course intends to expose students with fundamental computational tools in AI. The course intends to draw a balanced picture between automated reasoning and machine learning. The technical approaches discussed will include mathematical programming, planning, constraint satisfaction, multi-agent modeling, reinforcement learning and statistical machine learning. Second, this course intends to motivate students with successful applications of artificial intelligence on problems that have real-world impact. We intend to cover successful applications of artificial intelligence in computational sustainability, citizen science, and AI-driven scientific discovery.

Classes will consist of instructor presentations, student presentations, a course project, and group discussions. The first few lectures consist of introductions to basic computational tools, such as constraint programming, probabilistic inference, supervised and unsupervised learning, etc. Then the course will move to student-led discussions on successful integrations of automated reasoning and machine learning. Students are expected to (1) read, discuss, and present research papers, (2) complete a semester-long class project in groups, (3) review and comment on several class project proposals from other groups.

Prerequisites

Basic knowledge of linear algebra and calculus, a basic course in probability and statistics (e.g., STAT301/350/416, CS373), and basic programming skills (e.g., CS182) are required. Students without this background should have a discussion with the instructor prior to registering the course.

Target Students

Graduate or senior undergraduate students with interest in machine learning, data mining and artificial intelligence in general. This course also welcomes students from related fields, such as agriculture, economics, applied math, physics, chemistry, and engineering, who are interested in using computational tools to solve real-world problems in their domain of interest.

Course Activities and Evaluation

Attendance: Attendance is highly encouraged. The instructor will include random in course small quizzes to account for attendance.

Course presentations: Each student needs to present at least one topic in the class. Students are encouraged to form teams in the presentation. The available topics can be seen in the syllabus section.

Course project: MOST important part of this course. AI is a practical field, so it cannot be emphasized more the importance of completing a project yourself! In addition, because this is a graduate-level course, one important aspect is basic scientific training, including asking the right questions, commenting others' work, literature review, experimental design, coding, scientific writing, and presentation skills. This can ONLY be trained with a real project. Each student is encouraged to lead in one research topic.

We provide a few research thrusts and datasets for your reference (see below). You are encouraged to choose a specific project within the overarching theme of one research thrust in the list, although you are free to choose any project at your will as long as it relates to AI for scientific discovery and design. The goal is to nurture GROUND-BREAKING course projects, which have potentials to be developed into innovative research papers in the future. Course projects outside of the suggested thrusts will receive less mentoring from the instructors and the TAs, and therefore are less preferred. We encourage you to combine your domain of expertise with AI. To guide you through the project, we split the entire process into five parts: proposal, peer review, mid-term report, final report and presentation.

Course project proposal: the proposal will be evaluated by intellectural merit, broader impact, and tractability (same creteria for NSF proposals). The instructor DO respect that it is a course project, so the bar is much lower. However, the following three aspects are emphasized equally: (i) intellectural merit: how does the project advance machine learning (or your understanding on machine learning); (ii) broad impact: how does the course project bring impact to a practical field via machine learning? (iii) tractability: is this proposal tractable (as a one-semester course project)? [grading rubrics will be posted on Brightspace.]

Course project reivews: Each student is asked to review at least three proposals of others. The student is asked to review proposals based on intellectural merit, broader impact, and tractability. Peer reviews are safety belts for other students. Unrealistic proposals should be flagged out. We will also host review panels in the class, where reviewers discuss project proposals and give panel summary reviews. Gaming does not work: the grading of the original propsal will NOT be affected by how other students review your proposal. [grading rubrics will be posted on Brightspace.]

Course project mid-term progress report: Each group is expected to submit a progress report by the deadline. This is to ensure that all projects are progressing on the right track. [grading rubrics will be posted on Brightspace.]

Course project final report / presentation: The final report and presentation will be graded in a similar way as conference papers (presentations) by TAs and the instructor jointly (although the bar is much lower). [grading rubrics will be posted on Brightspace.]

Grading Scale

Syllabus (Tentative)

Course Project Thrusts

Thrust 1: stochastic optimization: encoding machine learning for decision-making

In data-driven decision-making, we have to reason about the optimal policy of a system given a stochastic model learned from data. For example, one can use a machine learning model to capture the traffic dynamics of a road network. The decision-making problem is: given the traffic dynamics learned from data, what is the most efficient way to travel between a pair of locations? Notice that the solution can change dynamically, depending on the shift in traffic dynamics. As another example in Physics, machine learning models have been used to predict the band-gap of many metal alloy materials. The decision-making problem is: given the machine learning model, what is the best alloy, which is both cheap to synthesize and has a good band-gap property?

The aforementioned examples are stochastic optimization problems, which make robust interventions that maximize the ``expectation'' of stochastic functions learned from data. It arises naturally in many applications ranging from economics, operational research, and artificial intelligence. Stochastic optimization combines two intractable problems, one of which is the inner probablistic inference problem to compute the expectation across exponentially many probabilistic outcomes, and the other of which is the outer optimization problem to search for the optimal policy.

Research questions: (i) if the inner machine learning model is a decision tree, can you compute the optimal policy in polynomial time? How? (ii) What if the inner machine learning model is a logistic regression, a linear SVM, a kernerized SVM, a random forest, or a probabilistic graphical model? (iii) What if the machine learning model is temporal, such as a recurrent neural netowrk or a LSTM? (iv) In case the inner probabilistic inference problem is intractable, existing approaches to solve stochastic optimization problems approximate the intractable probabilistic inference sub-problems either in variational forms, or via the empirical mean of pre-computed, fixed samples. There is also a recent approach which approximates the intractable sub-problems with optimization queries, subject to randomized constraints (see following papers). How does various approximation schemes of the inner machine learning models affect the overall solution quality of the stochastic optimization problem? (v) Suppose we are solving one stochastic optimization problem for a specific application, can we adapt existing approximation schemes in any way to fit the problem instance for better results?

Papers:

Jinzhao Li, Nan Jiang and Yexiang Xue.
Solving Satisfiability Modulo Counting for Symbolic and Statistical AI Integration with Provable Guarantees.
In Proceedings of the Thirty-Eighth AAAI Conference on Artificial Intelligence (AAAI), 2024. [ArXiv] [YouTube]

Yexiang Xue, Zhiyuan Li, Stefano Ermon, Carla P. Gomes, Bart Selman.
Solving Marginal MAP Problems with NP Oracles and Parity Constraints
In the Proceedings of the 29th Annual Conference on Neural Information Processing Systems (NIPS), 2016. [pdf] [spotlight video]

Anton J. Kleywegt, Alexander Shapiro, and Tito Homem-de Mello.
The sample average approximation method for stochastic discrete optimization.
SIAM Journal on Optimization, 2002. [pdf]

Miguel Á. Carreira-Perpiñán and Geoffrey E. Hinton.
On contrastive divergence learning.
AISTATS, 2005. [pdf]

Martin Dyer and Leen Stougie.
Computational complexity of stochastic programming problems. Mathematical Programming, 2006. [springer]

John D. Lafferty, Andrew McCallum, and Fernando C. N. Pereira.
Conditional random fields: Probabilistic models for segmenting and labeling sequence data. In Proceedings of the Eighteenth International Conference on Machine Learning, ICML, 2001. [pdf]

Stefano Ermon, Carla Gomes, Ashish Sabharwal, and Bart Selman.
Taming the Curse of Dimensionality: Discrete Integration by Hashing and Optimization
In Proc. 30th International Conference on Machine Learning (ICML) 2013. [pdf]

Carla P. Gomes, Ashish Sabharwal, Bart Selman.
Near-Uniform Sampling of Combinatorial Spaces Using XOR Constraints.
NIPS 2006. [pdf]

Carla P. Gomes, Willem Jan van Hoeve, Ashish Sabharwal, Bart Selman.
Counting CSP Solutions Using Generalized XOR Constraints.
AAAI 2007. [pdf]

Yexiang Xue*, Xiaojian Wu*, Bart Selman, and Carla P. Gomes.
XOR-Sampling for Network Design with Correlated Stochastic Events.
In Proc. 26th International Joint Conference on Artificial Intelligence (IJCAI), 2017. [pdf]
* indicates equal contribution.

Yexiang Xue, Xiaojian Wu, Dana Morin, Bistra Dilkina, Angela Fuller, J. Andrew Royle, and Carla Gomes.
Dynamic Optimization of Landscape Connectivity Embedding Spatial-Capture-Recapture Information.
In Proc. 31th AAAI Conference on Artificial Intelligence (AAAI), 2017. [pdf] [supplementary materials]

Thrust 2: embedding physical constraints into deep neural networks

The emergence of large-scale data-driven machine learning and optimization methodology has led to successful applications in areas as diverse as finance, marketing, retail, and health care. Yet, many application domains remain out of reach for these technologies, when applied in isolation. In the area of medical robotics, for example, it is crucial to develop systems that can recognize, guide, support, or correct surgical procedures. This is particularly important for next-generation trauma care systems that allow life-saving surgery to be performed remotely in presence of unreliable bandwidth communications. For such systems, machine learning models have been developed that can recognize certain commands and procedures, but they are unable to learn complex physical or operational constraints. Constraint-based optimization methods, on the other hand, would be able to generate feasible surgical plans, but currently, have no mechanism to represent and evaluate such complex environments. To leverage the required capabilities of both technologies, we have to find an integrated method that embeds constraint reasoning in machine learning.

The authors of the first paper below proposed an approach, which provides a scalable method for machine learning over structured domains. The core idea is to augment machine learning algorithms with a constraint reasoning module that represents physical or operational requirements. Specifically, the authors propose to embed decision diagrams, a popular constraint reasoning tool, as a fully-differentiable layer in deep neural networks. By enforcing the constraints, the output of generative models can now provide assurances of safety, correctness, and/or fairness. Moreover, this approach enjoys a smaller modeling space than traditional machine learning approaches, allowing machine learning algorithms to learn faster and generalize better.

Research questions: (i) are there any other ways to enforce physical constraints other than using a decision diagram in the seminal work? (ii) What if the constraints are too complicated which cannot be fully captured by a decision diagram? (iii) In a specific applicational domain, is there a better way to encode constraints? (iv) Does enforcing physical constraints make machine learning easier or more difficult? Can you quantify the difference? (v) Can we apply this idea in natural language processing, computer vision, reinforcement learning, etc? (vi) Ethics and fairness in machine learning are being discussed in our community. Can we use this technique to guarantee the ethics and/or the fairness of a machine learning model?

Papers:

Nan Jiang, Maosen Zhang, Willem-Jan van Hoeve, Yexiang Xue.
Constraint Reasoning Embedded Structured Prediction.
In Journal of Machine Learning Research (JMLR), 23(345):1--40, 2022.[JMLR website][slides]

Maxwell Jacobson and Yexiang Xue.
Integrating Spatial Reasoning into Neural Generative Models for Design Production.
In the Artificial Intelligence journal, Volume 339, 104257, 2025. [DOI][ArXiv preprint][slides]

Yexiang Xue, Willem-Jan van Hoeve.
Embedding Decision Diagrams into Generative Adversarial Networks.
In Proc. of the Sixteenth International Conference on the Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR), 2019. [springer]

Md Masudur Rahman, Natalia Sanchez-Tamayo, Glebys Gonzalez, Mridul Agarwal, Vaneet Aggarwal, Richard M. Voyles, Yexiang Xue, and Juan Wachs.
Transferring Dexterous Surgical Skill Knowledge between Robots for Semi-autonomous Teleoperation.
In ROMAN, 2019. [pdf]

Naveen Madapana, Md Masudur Rahman, Natalia Sanchez-Tamayo, Mythra V. Balakuntala, Glebys Gonzalez, Jyothsna Padmakumar Bindu, L. N. Vishnunandan Venkatesh, Xingguang Zhang, Juan Barragan Noguera, Thomas Low, Richard M. Voyles, Yexiang Xue, and Juan Wachs
DESK: A Robotic Activity Dataset for Dexterous Surgical Skills Transfer to Medical Robots.
In IROS, 2019. [pdf]

Matt J. Kusner, Brooks Paige, José Miguel Hernández-Lobato.
Grammar Variational Autoencoder.
In Proceedings of the 34th International Conference on Machine Learning, ICML, 2017. [pdf]

Chenglong Wang, Kedar Tatwawadi, Marc Brockschmidt, Po-Sen Huang, Yi Mao, Oleksandr Polozov, Rishabh SinghRobust
Text-to-SQL Generation with Execution-Guided Decoding
[pdf]

Kevin Lin, Ben Bogin, Mark Neumann, Jonathan Berant, Matt Gardner
Grammar-based Neural Text-to-SQL Generation
[ArXiv]

Thrust 3: machine learning for scientific discovery and/or social good

Machine learning models have defeated the brightest mind in this world (see the story of AlphaGo). Now, instead of using this technology for game playing, can we harness the tremendous progress in AI and machine learning to make our world a better place? In particular, I am curious at problems that have attracted the smartest minds of man kind historically -- the discovery of new science. Besides scientific discovery, can we use machine learning to create positive social impact?

If you think about it: in AlphaGo, machine learning is used to find a strategy in a highly combinatorial space (all possible moves of Go), which beats all opponent's strategies. The problem is similar for scientific discovery, except that we are now playing Go with nature. For example, in materials discovery, we would like to find the best material in a highly complex space (all possible materials compositions) which enjoys the best properties. Should the strategy which was proven successful for Go work for scientific discovery (and/or AI for social good)?

I am listing a few example papers below in which machine learning are used successfully for scientific discovery and for social good. I hope this can motivate you to discover a good applicational area of machine learning. The key to the success is to combine your domain of expertise with machine learning.

Papers:

Nan Jiang and Yexiang Xue.
Symbolic Regression via Control Variable Genetic Programming.
In Proceedings of the 2022 European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML-PKDD), 2023. [pdf][slides]

Yexiang Xue, Md Nasim, Maosen Zhang, Cuncai Fan, Xinghang Zhang, Anter El-Azab.
Physics Knowledge Discovery via Neural Differential Equation Embedding.
In Proceedings of 2021 European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML-PKDD), 2021. [pdf]

Chonghao Sima, Yexiang Xue.
LSH-SMILE: Locality Sensitive Hashing Accelerated Simulation and Learning.
In Proceedings of 35th Conference on Neural Information Processing Systems (NeurIPS), 2021. [pdf]

Md Nasim, Anter El-Azab, Xinghang Zhang, and Yexiang Xue.
End-to-end Phase Field Model Discovery Combining Experimentation, Crowdsourcing, Simulation and Learning.
In Proceedings of the Thirty-Sixth Annual Conference on Innovative Applications of Artificial Intelligence (IAAI-24), 2024. [pdf][YouTube]

Yexiang Xue, Junwen Bai, Ronan Le Bras, Brendan Rappazzo, Richard Bernstein, Johan Bjorck, Liane Longpre, Santosh K. Suram, Robert B. van Dover, John Gregoire, and Carla Gomes.
Phase-Mapper: An AI Platform to Accelerate High Throughput Materials Discovery.
In Proc. 29th Annual Conference on Innovative Applications of Artificial Intelligence (IAAI), 2017. [pdf][video 1][video 2][video 3]

Santosh K. Suram, Yexiang Xue, Junwen Bai, Ronan LeBras, Brendan H Rappazzo, Richard Bernstein, Johan Bjorck, Lan Zhou, R. Bruce van Dover, Carla P. Gomes, and John M. Gregoire.
Automated Phase Mapping with AgileFD and its Application to Light Absorber Discovery in the V-Mn-Nb Oxide System.
In American Chemical Society Combinatorial Science, Dec, 2016. [DOI][pdf][video 1][video 2][video 3]

Junwen Bai, Yexiang Xue, Johan Bjorck, Ronan Le Bras, Brendan Rappazzo, Richard Bernstein, Santosh K. Suram, Robert Bruce van Dover, John M. Gregoire, Carla P. Gomes.
Phase Mapper: Accelerating Materials Discovery with AI.
In AI Magazine, Vol. 39, No 1. 2018. [paper]

Yexiang Xue, Ian Davies, Daniel Fink, Christopher Wood, Carla P. Gomes.
Avicaching: A Two Stage Game for Bias Reduction in Citizen Science
In the Proceedings of the 15th International Conference on Autonomous Agents and Multiagent Systems (AAMAS), 2016. [pdf][supplementary materials][video]

Giuseppe Carleo and Matthias Troyer
Solving the quantum many-body problem with artificial neural networks.
In Science, 355, 2017. [website]

Ganesh Hegde and R. Chris Bowen
Machine-learned approximation to Density Functional Theory Hamiltons.
In Scientific Reports, 7, 2016. [ArXiv]

Graham Roberts, Simon Y. Haile, Rajat Sainju, Danny J. Edwards, Brian Hutchinson and Yuanyuan Zhu
Deep Learning for Semantic Segmentation of Defects in Advanced STEM Images of Steels.
Scientific Reports, volume 9, 2019. [website]

Academic Policies

Late policy

Assignments are to be submitted by the due date listed. Each person will be allowed three days of extensions which can be applied to any combination of assignments (homework/projects only; exams excluded) during the semester without penalty. After that, a late penalty of 15% per day will be assigned. The use of a partial day will be counted as a full day. Use of extension days must be stated explicitly at the time of the late submission (by accompanying email to ALL TAs and the instructor), otherwise, late penalties will apply. Extensions cannot be used after the final day of classes. Extension days cannot be rearranged after they are applied to a submission. Additional no-penalty late days may be introduced in the later part of the semester conditioned on the completion of the course evaluations (details to be finalized). Assignments, project reports, etc, will NOT BE accepted if they are more than five days late (and receive zero points). Additional extensions will be granted only due to serious and documented medical or family emergencies. Use the late days wisely!

Classroom engagement is extremely important and associated with your overall success in the course. The importance and value of course engagement and ways in which you can engage with the course content even if you are in quarantine or isolation, will be discussed at the beginning of the semester. Student survey data from Fall 2020 emphasized students’ views of in-person course opportunities as critical to their learning, engagement with faculty/TAs, and ability to interact with peers.

Only the instructor can excuse a student from a course requirement or responsibility. When conflicts can be anticipated, such as for many University-sponsored activities and religious observations, the student should inform the instructor of the situation as far in advance as possible. For unanticipated or emergency conflicts, when advance notification to an instructor is not possible, the student should contact the instructor/instructional team as soon as possible by email, through Brightspace, or by phone. In cases of bereavement, quarantine, or isolation, the student or the student’s representative should contact the Office of the Dean of Students via email or phone at 765-494-1747. Our course Brightspace includes a link to the Dean of Students under ‘Campus Resources.’

Academic honesty

• Unless stated otherwise, each student should write up their own solutions independently. You need to indicate the names of the people you discussed a problem with; ideally you should discuss with no more than two other people.
• NO PART OF THE STUDENT'S ASSIGMENT (PROJECT, NOTES, ETC) SHOULD BE COPIED FROM ANOTHER STUDENT OR FROM OTHER RESEARCHERS OR FROM THE WEB (Plagiarism). We encourage you to interact amongst yourselves: you may discuss and obtain help with basic concepts covered in lectures or the textbook, homework specification (but not solution), and general ideas of program implementation (but not the code). However, unless otherwise noted, work turned in should reflect your own efforts and knowledge. Sharing or copying solutions is unacceptable and could result in failure of this course. We use copy detection software, so do not copy code and make changes (either from the Web or from other students). You are expected to take reasonable precautions to prevent others from using your work.
• Any student not following these guidelines are subject to an automatic F (final grade).

Nondiscrimination Statement

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Accessbility

Purdue University strives to make learning experiences as accessible as possible. If you anticipate or experience physical or academic barriers based on disability, you are welcome to let me know so that we can discuss options. You are also encouraged to contact the Disability Resource Center at: drc@purdue.edu or by phone: 765-494-1247.

Mental Health/Wellness Statement

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If you’re struggling and need mental health services: Purdue University is committed to advancing the mental health and well-being of its students. If you or someone you know is feeling overwhelmed, depressed, and/or in need of mental health support, services are available. For help, such individuals should contact Counseling and Psychological Services (CAPS) at 765-494-6995 during and after hours, on weekends and holidays, or by going to the CAPS office on the second floor of the Purdue University Student Health Center (PUSH) during business hours.

Emergency Preparation

In the event of a major campus emergency, course requirements, deadlines and grading percentages are subject to changes that may be necessitated by a revised semester calendar or other circumstances beyond the instructor’s control. Relevant changes to this course will be posted onto the course website or can be obtained by contacting the instructors or TAs via email or phone. You are expected to read your @purdue.edu email on a frequent basis.

Other general course policies can be found here.

Resource

Datasets

eBird citizen scince dataset.

Synthetic and real datasets for materials discovery.

Dataset for the corridor-design problem and landscape optimization problem.

Remote sensing images (a code repository which contains code to download from Google Earth engine).

UCI Machine Learning Dataset.

Kaggle.

Online Resources

Machine learning:

• A First Encounter with Machine Learning by Max Welling
• Introduction to Machine Learning by Alex Smola and S.V.N. Vishwanathan
• A Course in Machine Learning by Hal Daume III
• Bayesian reasoning and machine learning by David Barber
• A tutorial by Andrew Moore

• The Matrix Cookbook by Kaare Brandt Petersen and Michael Syskind Pedersen
• Calculus by Gilbert Strang
• Linear Algebra by Gilbert Strang
• Introduction to Probability and Statistics by Jeremy Orloff and Jonathan Bloom

• The official Python Tutorial
• LeetCode