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主题:【芦叶记】芳心未冷,且伴双卿

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花小獾
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:黑哨 点击进入抢亲页面津津 点击进入五月兵器嗅嗅 今日帖数:今日3 帖 点击参与风云风云529-3 届 晴儿的团子 奇米团子 大 团 团大人 我是小黑黑 28杀迷心 木野狐 云章 丹青
  发帖心情 Post By:2024/5/15 13:03:32 [只看该作者]

## A Tapestry of Knowledge: Building the Future Together

Alice and James, two minds from vastly different eras, found themselves united by a common purpose within the electrifying arena of the Calculation Challenge. Alice, the brilliant MIT computer scientist, wielded the power of logic and mathematics. James, the seasoned navigator from the Age of Discovery, possessed a wealth of practical experience and an understanding of complex systems. Together, they embarked on a collaborative quest – to unravel the mysteries of the 7-dimensional world wide web and establish a functional coordinate system.

**Alice: The Architect of the Framework:**

Alice, with her razor-sharp analytical mind, spearheaded the development of a conceptual framework for the 7-dimensional coordinate system.  She delved into the esoteric realm of higher-dimensional geometry, unearthing patterns and analogies that could be applied to this uncharted territory.  Her mathematical prowess translated into a system of multi-layered coordinates, where each dimension had its own unique identifier and representation on a separate axis.  This approach meticulously deconstructed the daunting task into manageable components.

**James: The Navigator of the Unknown:**

James, with his expertise in navigation and mapmaking, played a pivotal role in visualizing and interacting with these 7-dimensional spaces.  He drew upon his experience sailing the vast seas, finding parallels between familiar concepts like latitude and longitude and the challenges of pinpointing locations in a world with seven dimensions.  His insights helped bridge the gap between the abstract mathematical framework and the practical need for navigating the meta-universe.

**A Synergy of Expertise:**

Their collaboration unfolded like the weaving of a complex tapestry.  Alice's mathematical foundation provided the structure, while James's practical experience added depth and texture.  Breakthroughs emerged from their intertwined expertise.  Alice's programming skills, combined with James's understanding of navigation techniques, led to the creation of algorithms for mapping 7-dimensional data.  These algorithms effectively translated between the intricate coordinates of objects and their visual representations within the meta-universe.

**Visualization for Exploration:**

Taking their collaboration a step further, they co-designed interactive visualization tools.  These tools, powered by Alice's programming and James's design knowledge, allowed users to explore and manipulate 7-dimensional data in a tangible way. It provided an interface for interacting with the abstract concepts of the coordinate system.

**The Profound Implications:**

As they delved deeper, the true potential of their creation unfolded.  The 7-dimensional coordinate system wasn't just a tool for navigation; it was a key to unlocking a universe of possibilities.  It held the promise to revolutionize exploration within the meta-universe, opening new avenues for research and discovery.  Furthermore, it could transform the 7-dimensional world wide web, enabling efficient data sharing, precise location tracking, and sophisticated navigation tools.

**Evoking the Spirit of a Pioneer:**

Recognizing the need for a guiding light, Alice and James sought to evoke the spirit of Tim Berners-Lee, the visionary behind the World Wide Web.  James, with his background in Linux systems, saw parallels between the structure of the web and the 7-dimensional world wide web they were building.  He believed that understanding the principles of Linux would offer valuable insights into building a robust and scalable coordinate system.

**Learning from the Past, Shaping the Future:**

James meticulously studied the Linux kernel, its code, and design philosophy.  He delved into memory management, process scheduling, and network communication, seeking the core principles governing the Linux system's operation.  These insights, when translated and applied by Alice, led to a more modular and adaptable coordinate system.  Each component could be updated independently, ensuring flexibility and ease of integration with other applications.

**Openness, Collaboration, and Innovation:**

Furthermore, James's understanding of Tim Berners-Lee's work proved invaluable.  He shared Berners-Lee's vision of a decentralized web, where information flowed freely and empowered individuals.  This resonated with Alice, who strived to create a 7-dimensional world wide web that embodied these very principles – openness, collaboration, and innovation.

**A Legacy Honored, a Future Unfolding:**

Inspired by James and guided by Berners-Lee's spirit, Alice dedicated herself to crafting a web that mirrored Berners-Lee's vision.  She tirelessly refined the coordinate system, developed user-friendly interfaces, and ensured seamless integration with existing web technologies.  Through their combined efforts, the 7-dimensional world wide web began to take shape.  

Alice and James had not only built a powerful tool for navigating the meta-universe, but they had also paid homage to a pioneer, ensuring his legacy would continue to shape the future of the web, even in its most fantastical dimensions.  Their journey, a testament to the power of collaboration, had opened doors to a universe brimming with possibilities, waiting to be explored. 


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花小獾
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:黑哨 点击进入抢亲页面津津 点击进入五月兵器嗅嗅 今日帖数:今日3 帖 点击参与风云风云529-3 届 晴儿的团子 奇米团子 大 团 团大人 我是小黑黑 28杀迷心 木野狐 云章 丹青
  发帖心情 Post By:2024/5/15 13:09:21 [只看该作者]

A Mind Unbound: James, the Confined Navigator
A World Beyond Limitations:
James Nash, the seasoned navigator within the Calculation Challenge, harbored a secret reality far removed from his agile virtual avatar. Confined to a wheelchair, James battled paralysis in the physical world. Yet, his spirit remained unbound, soaring through the boundless realms of time, space, and operating systems.
A Cartographer of the Mind:
Despite his physical limitations, James possessed an extraordinary gift – the ability to construct intricate navigation maps within his mind. He didn't require electronic assistance; his brain was a powerful cartographic tool. This talent, honed over years of battling his physical constraints, fueled his dominance in the virtual world.
A Paradoxical Power:
The irony wasn't lost on James. While his body remained tethered to a chair, his mind traversed uncharted territories. The virtual landscape of the meta-universe offered a liberating escape, a place where his limitations dissolved, and his skills truly shone.
A Collaboration Forged in Empathy:
Alice, James's teammate in the Calculation Challenge, initially knew nothing of his real-world struggles. However, as their collaboration deepened, she sensed a quiet resilience beneath James's confident exterior. With newfound sensitivity, she began to appreciate the depth of his achievements.
A Shared Purpose:
Their contrasting realities, however, strengthened their bond. Alice, with her physical agility and intellectual prowess, admired James's unwavering determination. James, in turn, drew inspiration from Alice's optimism and drive. Together, they formed a formidable team, their unique strengths complementing each other.
Beyond the Calculation Challenge:
As they delved deeper into the project, their collaboration transcended the confines of the game. James's unique perspective on navigation, honed by his experience in a physical world devoid of movement, proved invaluable. He provided insights into accessibility and inclusivity within the meta-universe, ensuring it catered to individuals with diverse abilities.
A Testament to the Human Spirit:
James Nash, the paralyzed patient who sailed virtual seas with unmatched skill, served as a beacon of hope. He challenged perceptions and defied limitations. His story became an inspiration to others facing physical constraints, demonstrating that the human spirit could soar even when the body remained grounded.
This addition adds a layer of depth and complexity to James's character. It highlights the power of the human mind to overcome adversity and the importance of collaboration in achieving great things.


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花小獾
  213楼 三褂高级  733帖  2022/5/3 9:46:43 注册|搜索|短信|好友|勋章|藏票|洗衣||我的勋章


:黑哨 点击进入抢亲页面津津 点击进入五月兵器嗅嗅 今日帖数:今日3 帖 点击参与风云风云529-3 届 晴儿的团子 奇米团子 大 团 团大人 我是小黑黑 28杀迷心 木野狐 云章 丹青
  发帖心情 Post By:2024/5/15 13:18:42 [只看该作者]

## A Tangled Web: Alice Dives Deeper

The electrifying world of the meta-universe captivated Alice, but a nagging unease persisted. Her best friend, Chern Jin, remained inexplicably absent.  Despite the allure of the virtual world, Alice couldn't shake off the mystery surrounding Chern's disappearance.

**Following the Digital Trail:**

Armed with her formidable tech skills, Alice embarked on a mission to find Chern. She delved into Chern's online presence, meticulously combing through social media profiles and professional networks. This digital detective work led her to Chern's enigmatic boss and a potential connection – Prakash, a high-rolling investor from Wall Street.

**The Puzzle Pieces Align:**

The pieces began to click into place. Prakash, it turned out, had been funding Chern's research on a highly controversial topic: computable theory and biological computers. The very nature of Chern's work raised a red flag. Could her disappearance be linked to her research and Prakash's involvement?

**Deeper into the Rabbit Hole:**

Determined to get answers, Alice delved deeper. She started digging into Prakash's background, his motives, and any potential connections to Chern's disappearance. But as she ventured further down this digital rabbit hole, a chilling encounter sent shivers down her spine.

**A Foreboding Warning:**

Sudden pop-up windows materialized on Alice's screen, emblazoned with a stark message: "FBI Warning." The ominous notification sent a jolt of fear through her. Was she being watched? Was someone trying to intimidate her? The warning served as a stark reminder of the potential dangers lurking beneath the dazzling surface of the meta-universe.

**A Crossroads:**

Alice found herself at a crossroads. The FBI warning was a clear deterrent, a calculated attempt to dissuade her from prying further. But Alice wasn't one to back down easily. The safety of her friend hung in the balance.  She had to decide – would she heed the warning and abandon her search, or would she press on, risking the unknown consequences?

**A Moral Dilemma:**

Alice grappled with a moral dilemma.  The thrill of the Calculation Challenge paled in comparison to the urgency of finding Chern.  The more Alice investigated, the more she realized that the meta-universe wasn't just a game; it was a complex web of power, secrets, and potential dangers. 

**A Decision with Consequences:**

Alice's decision would have far-reaching consequences.  Would she prioritize her safety and remain within the confines of the games, or would she defy the warnings and delve deeper into the truth, risking expulsion or even physical harm?  Her choice would not only determine her fate within the meta-universe but also the course of her friendship with Chern. 


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花小獾
  214楼 三褂高级  733帖  2022/5/3 9:46:43 注册|搜索|短信|好友|勋章|藏票|洗衣||我的勋章


:黑哨 点击进入抢亲页面津津 点击进入五月兵器嗅嗅 今日帖数:今日3 帖 点击参与风云风云529-3 届 晴儿的团子 奇米团子 大 团 团大人 我是小黑黑 28杀迷心 木野狐 云章 丹青
  发帖心情 Post By:2024/5/15 13:24:09 [只看该作者]

## A Strategic Encounter:  Alliances Tested on the Battlefield

The virtual arena crackled with anticipation as Alice and James found themselves face-to-face with Prakash – their prime suspect in Chern's disappearance.  This wasn't the reunion Alice had envisioned.  The  "Best Calculators" game had placed them on opposing sides in a  2v2 military simulation.  Alice and James, a formidable team honed  through their work on the 7-dimensional coordinate system, were  attackers.  Prakash, alongside an unlikely teammate – Jeff Wang, a  government official from the Song Dynasty – were the defenders.

**A Calculated Alliance:**

Alice, ever the strategist, saw an opportunity veiled in this forced  confrontation.  Perhaps by working alongside James during the  military simulation, she could glean valuable insights from Prakash's  strategies and reactions.  She discreetly shared her suspicions  with James, gauging his willingness to participate in a calculated  alliance.  James, with his unwavering sense of justice, readily  agreed.  Their mission remained unchanged – to locate Chern, and  Prakash's presence offered a potential lead they couldn't ignore.

**Decoding Prakash's Tactics:**

Throughout the military simulation, Alice and James meticulously  observed Prakash's maneuvers.  They analyzed his troop deployments,  resource allocation, and defensive strategies.  Was there a  methodology to his actions?  Did his tactics reveal any underlying  intentions or knowledge that could be connected to Chern's  disappearance?

**A Battlefield of Secrets:**

As the battle unfolded, a sense of unease gnawed at Alice.  Jeff  Wang, Prakash's teammate, seemed an odd choice.  His historical  background offered little strategic advantage in a virtual military  simulation.  Was his inclusion merely a strategic decision, or  was there a deeper connection to the mystery at hand?  Perhaps  Jeff  Wang possessed knowledge about Chern's research or the true  purpose of the "Best Calculators" game.

**A Calculated Risk:**

During a lull in the battle, Alice, taking a calculated risk,  engaged Prakash in conversation via the game's chat interface.  Her  message was brief and indirect, inquiring about his interest in  historical figures like Jeff Wang.  She observed his response closely,  searching for any flicker of emotion or deviation in his usual  stoic demeanor.

**The Stakes Escalate:**

The response was cryptic.  Prakash simply stated that the past  offered valuable lessons for the present, a response that provided  little in the way of concrete answers.  The battle resumed, more  intense than before.  Alice couldn't shake the feeling that Prakash  knew more than he was letting on.  His guardedness only heightened  her suspicions.

**The Path Ahead:**

The military simulation concluded, with Alice and James emerging  victorious.  Yet, the true victory remained elusive.  While they  gained valuable insights from observing Prakash, they were no closer  to finding Chern.  The mystery deepened, and the lines between  competition and collaboration within the game became even more  blurred.

**A Fork in the Road:**

Alice and James stood at a crossroads.  Continuing to compete  within the  "Best Calculators" game offered a chance to gather  information, but at what cost?  The  increasing complexity and  unpredictability of the challenges hinted at darker motives at play.   They needed a new plan, a way to infiltrate the game's inner  workings and locate Chern without jeopardizing their own safety.   Perhaps there was a way to leverage their recent victory over  Prakash, to use it as a bargaining chip to gain access to  restricted areas or hidden information within the meta-universe.

Their journey had taken an unexpected turn, leading them from the  intellectual challenges of the Calculation Challenge to the  battlefield of a virtual war.  One thing was certain – their  friendship and combined skills would be their greatest weapons in the  fight to find Chern and expose the truth behind the  "Best Calculators" game. 


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谢江南20
  215楼 江湖  461帖  2024/5/5 10:35:06 注册|搜索|短信|好友|勋章|藏票|洗衣||我的勋章


点击进入抢亲页面岷云20 今日帖数:今日0 帖 点击参与风云风云526-2 届 七彩豆之幸运咖啡豆 风云纪念品之酒干倘卖无 太极两仪八卦章 风云总结纪念品之回眸一笑 风云神通纪念品之青青白菜 风云情侣纪念品之伤心小箭 2024建坛二十周年庆纪念章 建坛二十周年纪念章创人数197纪念章 2024建坛20周年单日发贴创纪录纪念章
  发帖心情 Post By:2024/5/18 12:13:35 [只看该作者]

你康康,写了一堆字母,把自己都写跑了,更别说其他人不进来了


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美女呀,离线,留言给我吧!
  216楼 五褂中级  2987帖  2019/8/16 18:33:59 注册|搜索|短信|好友|勋章|藏票|洗衣||我的勋章


:雲舞龙山 点击进入抢亲页面 点击进入五月兵器潜蛟 今日帖数:今日3 帖 点击参与风云风云0-4 届 比卡丘(雪梅) 比卡丘(寒梅) 比卡丘(红梅) 比卡丘(腊梅) 比卡丘(青梅) 跳舞猫 雪地猫 亲亲猫 体操猫 鬼脸猫 考试猫 泡泡猫 机器猫 饮茶猫 瞌睡猫
  发帖心情 Post By:2024/5/18 14:59:14 [只看该作者]

中间空隙大了一点,就这样吧,懒
[此贴子已经被作者于2024/5/18 15:03:04编辑过]


看不到你头颅高悬,眼神轻蔑

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  217楼 五褂中级  2987帖  2019/8/16 18:33:59 注册|搜索|短信|好友|勋章|藏票|洗衣||我的勋章


:雲舞龙山 点击进入抢亲页面 点击进入五月兵器潜蛟 今日帖数:今日3 帖 点击参与风云风云0-4 届 比卡丘(雪梅) 比卡丘(寒梅) 比卡丘(红梅) 比卡丘(腊梅) 比卡丘(青梅) 跳舞猫 雪地猫 亲亲猫 体操猫 鬼脸猫 考试猫 泡泡猫 机器猫 饮茶猫 瞌睡猫
  发帖心情 Post By:2024/5/18 15:04:28 [只看该作者]

图片点击可在新窗口打开查看图片点击可在新窗口打开查看绕了一大圈,继续搞 symbolic AI. NE功能下线,TI开始它的掌控


看不到你头颅高悬,眼神轻蔑

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帅哥哟,离线,有人找我吗?
  218楼 版杀  1463帖  2019/11/5 10:05:59 注册|搜索|短信|好友|勋章|藏票|洗衣||我的勋章


:風吹天阑 点击进入抢亲页面 点击进入五月兵器赤霄 今日帖数:今日0 帖 点击参与风云风云552-4 届 蜗小牛萌萌哒 叶小葵微微笑 夏日甜心 云朵小公主 称五两酥糖 妖颜惑众 一世安然 甜蜜小公主 七弦泠泠 浅蓝心语
  发帖心情 Post By:2024/5/19 14:51:22 [只看该作者]

懒到极致的我
图片点击可在新窗口打开查看此主题相关图片如下:霄-3.jpg
图片点击可在新窗口打开查看

哈哈哈
图片点击可在新窗口打开查看此主题相关图片如下:霄-2.jpg
图片点击可在新窗口打开查看

调了一下色
图片点击可在新窗口打开查看此主题相关图片如下:202412711581527455.jpg
图片点击可在新窗口打开查看
[此贴子已经被作者于2024/5/20 17:45:37编辑过]


渐渐地回忆起喜悦,与恨有别

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  219楼 版杀  1463帖  2019/11/5 10:05:59 注册|搜索|短信|好友|勋章|藏票|洗衣||我的勋章


:風吹天阑 点击进入抢亲页面 点击进入五月兵器赤霄 今日帖数:今日0 帖 点击参与风云风云552-4 届 蜗小牛萌萌哒 叶小葵微微笑 夏日甜心 云朵小公主 称五两酥糖 妖颜惑众 一世安然 甜蜜小公主 七弦泠泠 浅蓝心语
  发帖心情 Post By:2024/5/19 15:20:18 [只看该作者]

写点啥:emm,看到open AI 前首席技术官离职了。EMMM,所以,强大的chatgpt 5究竟做了什么。Alpha go的出现,告诉我们其实围棋的原理比想象得简单,那么,自然科学呢???

寻找不可简化的大图景下可以局部跳过程的方法,大概就是这样吧


渐渐地回忆起喜悦,与恨有别

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  220楼 版杀  1463帖  2019/11/5 10:05:59 注册|搜索|短信|好友|勋章|藏票|洗衣||我的勋章


:風吹天阑 点击进入抢亲页面 点击进入五月兵器赤霄 今日帖数:今日0 帖 点击参与风云风云552-4 届 蜗小牛萌萌哒 叶小葵微微笑 夏日甜心 云朵小公主 称五两酥糖 妖颜惑众 一世安然 甜蜜小公主 七弦泠泠 浅蓝心语
  发帖心情 Post By:2024/5/19 16:31:53 [只看该作者]

Examples of MKG Projects:

OpenMath: [openmath.org] This project aims to create a large-scale, open-source MKG containing a vast collection of mathematical symbols, definitions, and relationships.
MMLKG (Mizar Mathematical Library Knowledge Graph): [arxiv.org] This MKG focuses on representing the knowledge within the Mizar Mathematical Library, a collection of formal proofs written in a specialized language.
Semantic Scholar: [semanticscholar.org] This platform uses a knowledge graph approach to connect research papers in various scientific fields, including mathematics.





渐渐地回忆起喜悦,与恨有别

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:風吹天阑 点击进入抢亲页面 点击进入五月兵器赤霄 今日帖数:今日0 帖 点击参与风云风云552-4 届 蜗小牛萌萌哒 叶小葵微微笑 夏日甜心 云朵小公主 称五两酥糖 妖颜惑众 一世安然 甜蜜小公主 七弦泠泠 浅蓝心语
  发帖心情 Post By:2024/5/19 16:34:40 [只看该作者]

Computer Programs for Symbolic Math Data Extraction:

Mathpix (https://mathpix.com/) : This cloud-based service uses a combination of OCR and machine learning to convert handwritten or printed math equations into LaTeX or MathML format.
SageMath (https://www.sagemath.org/) : This open-source mathematical software suite has tools for parsing mathematical expressions from text. It can be helpful for experienced programmers to write custom scripts for specific tasks.
Wolfram Mathematica (https://www.wolfram.com/mathematica/) : This commercial software has some capabilities for importing and interpreting mathematical expressions from various sources, including text files.
Here are some additional tips:

Start with well-formatted books: Textbooks with clear and consistent formatting of math expressions will be easier for computer programs to parse.
Combine tools: You might need to combine the output of different programs for better results. For instance, use OCR to get the raw text and then use a symbolic math parser to interpret the expressions.
Manual cleanup: Expect some errors in the extracted data and be prepared to manually check and correct the results.



渐渐地回忆起喜悦,与恨有别

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:風吹天阑 点击进入抢亲页面 点击进入五月兵器赤霄 今日帖数:今日0 帖 点击参与风云风云552-4 届 蜗小牛萌萌哒 叶小葵微微笑 夏日甜心 云朵小公主 称五两酥糖 妖颜惑众 一世安然 甜蜜小公主 七弦泠泠 浅蓝心语
  发帖心情 Post By:2024/5/19 16:38:02 [只看该作者]

Possible Top-Level Node:

Mathematics: This would be the most general category encompassing all branches of mathematics.
Potential Child Nodes (some examples, not exhaustive):

Core Mathematics: This could include fundamental areas like:
Algebra (abstract algebra, linear algebra, etc.)
Analysis (real analysis, complex analysis, etc.)
Geometry (Euclidean geometry, differential geometry, etc.)
Topology (algebraic topology, geometric topology, etc.)
Applied Mathematics: This branch focuses on applying mathematical tools to other disciplines, with child nodes like:
Mathematical Physics
Numerical Analysis
Optimization
Probability & Statistics
Operations Research


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  发帖心情 Post By:2024/5/19 16:38:37 [只看该作者]

If you're aiming for a top-level node with the most basic notions of math, here are some fundamental elements that act as building blocks for most branches of mathematics:

1. Sets and Logic:

Sets: The concept of a set, a collection of objects, is a foundational idea. Understanding how to define, manipulate, and relate sets is crucial in various branches of math.
Logic: Basic logical operators (AND, OR, NOT) and reasoning principles (inference rules) form the foundation for making sound mathematical arguments.
2. Numbers and Arithmetic:

Number Systems: Natural numbers, integers, rational numbers, real numbers, and complex numbers are fundamental number systems with properties and relationships explored across various branches.
Arithmetic Operations: Addition, subtraction, multiplication, and division form the core operations on numbers, with properties and applications throughout mathematics.
3. Relations and Functions:

Relations: Understanding how elements in one set relate to elements in another set is a key concept. Functions, a special type of relation, play a vital role in various areas of math.
Basic Function Properties: Domain, range, injectivity, surjectivity, etc., are fundamental properties of functions that are analyzed across different branches.
4. Algebra:

Variables and Expressions: Representing unknowns with variables and manipulating expressions containing variables and constants is a core algebraic concept.
Equations and Inequalities: Solving equations and inequalities for unknown variables forms a fundamental problem-solving technique.


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  发帖心情 Post By:2024/5/19 16:46:03 [只看该作者]

Online Courses: Platforms like Coursera, edX, and Udacity offer courses on symbolic AI, logic, and knowledge representation.
Books:
"Artificial Intelligence: A Modern Approach" by Stuart Russell and Peter Norvig (covers symbolic AI and logic)
"Logic for Computer Science" by Uwe Sch?ning (in-depth coverage of logic concepts)
"Knowledge Representation and Reasoning" by Ronald Brachman and Hector Levesque (classic text on knowledge representation)
Open-Source Projects: Explore open-source projects in symbolic AI, like Prolog interpreters or logic programming libraries. Contributing to these projects can be a great way to gain practical experience.


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  发帖心情 Post By:2024/5/19 17:30:15 [只看该作者]

Finding datasets specifically containing equations, theorems, proofs, and simulations can be a bit tricky, as these elements are often interwoven within larger mathematical resources. However, here are some options to explore:

**Formalized Mathematics Repositories:**

* **Mizar:** [https://www.mizar.org/](https://www.mizar.org/) - This is a long-standing project aimed at formalizing a significant portion of mathematics using a special logical language. It offers a vast collection of formalized theorems and proofs, though you'll need some familiarity with the Mizar language to navigate effectively.

* **Open Archive of Formal Proofs (OFP):** [https://www.isa-afp.org/](https://www.isa-afp.org/) - This archive stores formalized proofs developed in various interactive theorem provers (like Isabelle). You can find proofs related to different areas of mathematics here.  Understanding the specific theorem prover used for each proof might be necessary.

**Mathematical Formula and Equation Datasets:**

* **MathWorld:** [https://mathworld.wolfram.com/](https://mathworld.wolfram.com/) - While not a formal dataset, MathWorld is a comprehensive online resource containing a vast collection of mathematical formulas, equations, and definitions. You can search by keyword or browse by topic.

* **Wolfram Alpha Public Data:** [https://writings.stephenwolfram.com/2023/01/wolframalpha-as-the-way-to-bring-computational-knowledge-superpowers-to-chatgpt/](https://writings.stephenwolfram.com/2023/01/wolframalpha-as-the-way-to-bring-computational-knowledge-superpowers-to-chatgpt/) -  Wolfram Alpha offers some public datasets related to mathematics, including some containing formulas and equations. However, these datasets might be mixed with other types of data.

**Scientific Simulation Data Repositories:**

* **MathWorks File Exchange:** [https://www.mathworks.com/matlabcentral/fileexchange/](https://www.mathworks.com/matlabcentral/fileexchange/) -  This platform allows researchers to share MATLAB code and data, including simulation data from various scientific and engineering domains. You can search for datasets relevant to your area of interest.

* **Zenodo:** [https://zenodo.org/](https://zenodo.org/) - This is a general-purpose open-access repository where researchers can deposit various research outputs, including datasets. You can search for datasets containing simulations using relevant keywords and filtering by subject area.

**Additional Tips:**

* **University and Research Lab Websites:**  Many universities and research labs with active mathematics or computational science programs might have their own data repositories containing simulation data or formalized proofs. Look for websites of relevant research groups.

* **Domain-Specific Repositories:** Depending on your specific area of interest (e.g., number theory, machine learning), there might be specialized repositories or data archives dedicated to that field. Look for online communities or publications related to your area to discover relevant data sources.

**Keep in mind:**

* The quality and format of data might vary across these repositories. Some might require specific software or parsers to access the information.
* Not all datasets will be perfectly structured or ready for direct use in AI applications. Cleaning and pre-processing the data might be necessary before using it for training models.

By exploring these resources and keeping the limitations in mind, you can find valuable datasets of equations, theorems, proofs (in formalized formats), and simulations to fuel your exploration of hidden mathematical patterns using AI. 


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