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๐Š-๐Œ๐ž๐š๐ง๐ฌ ๐‚๐ฅ๐ฎ๐ฌ๐ญ๐ž๐ซ๐ข๐ง๐  ๐„๐ฑ๐ฉ๐ฅ๐š๐ข๐ง๐ž๐ - ๐Ÿ๐จ๐ซ ๐›๐ž๐ ๐ข๐ง๐ง๐ž๐ซ๐ฌ

๐–๐ก๐š๐ญ ๐ข๐ฌ ๐Š-๐Œ๐ž๐š๐ง๐ฌ?
Itโ€™s an unsupervised machine learning algorithm that automatically groups your data into K similar clusters without labels. It finds hidden patterns using distance-based similarity.

๐ˆ๐ง๐ญ๐ฎ๐ข๐ญ๐ข๐ฏ๐ž ๐ž๐ฑ๐š๐ฆ๐ฉ๐ฅ๐ž:
You run a mall. Your data has:
โ€บ Age
โ€บ Annual Income
โ€บ Spending Score

K-Means can divide customers into:
โคท Budget Shoppers
โคท Mid-Range Customers
โคท High-End Spenders

๐‡๐จ๐ฐ ๐ข๐ญ ๐ฐ๐จ๐ซ๐ค๐ฌ:
โ‘  Choose the number of clusters K
โ‘ก Randomly initialize K centroids
โ‘ข Assign each point to its nearest centroid
โ‘ฃ Move centroids to the mean of their assigned points
โ‘ค Repeat until centroids donโ€™t move (convergence)

๐Ž๐›๐ฃ๐ž๐œ๐ญ๐ข๐ฏ๐ž:
Minimize the total squared distance between data points and their cluster centroids
๐‰ = ฮฃโ€–๐ฑแตข - ฮผโฑผโ€–ยฒ
Where ๐ฑแตข = data point, ฮผโฑผ = cluster center

๐‡๐จ๐ฐ ๐ญ๐จ ๐ฉ๐ข๐œ๐ค ๐Š:
Use the Elbow Method
โคท Plot K vs. total within-cluster variance
โคท The โ€œelbowโ€ in the curve = ideal number of clusters

๐‚๐จ๐๐ž ๐„๐ฑ๐š๐ฆ๐ฉ๐ฅ๐ž (๐’๐œ๐ข๐ค๐ข๐ญ-๐‹๐ž๐š๐ซ๐ง):

from sklearn.cluster import KMeans
X = [[1, 2], [1, 4], [1, 0], [10, 2], [10, 4], [10, 0]]
model = KMeans(n_clusters=2, random_state=0)
model.fit(X)
print(model.labels_)
print(model.cluster_centers_)


๐๐ž๐ฌ๐ญ ๐”๐ฌ๐ž ๐‚๐š๐ฌ๐ž๐ฌ:
โคท Customer segmentation
โคท Image compression
โคท Market analysis
โคท Social network analysis

๐‹๐ข๐ฆ๐ข๐ญ๐š๐ญ๐ข๐จ๐ง๐ฌ:
โ€บ Sensitive to outliers
โ€บ Requires you to predefine K
โ€บ Works best with spherical clusters

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๐—ฃ๐—ฟ๐—ถ๐—ป๐—ฐ๐—ถ๐—ฝ๐—ฎ๐—น ๐—–๐—ผ๐—บ๐—ฝ๐—ผ๐—ป๐—ฒ๐—ป๐˜ ๐—”๐—ป๐—ฎ๐—น๐˜†๐˜€๐—ถ๐˜€ (๐—ฃ๐—–๐—”)
๐—ง๐—ต๐—ฒ ๐—”๐—ฟ๐˜ ๐—ผ๐—ณ ๐—ฅ๐—ฒ๐—ฑ๐˜‚๐—ฐ๐—ถ๐—ป๐—ด ๐——๐—ถ๐—บ๐—ฒ๐—ป๐˜€๐—ถ๐—ผ๐—ป๐˜€ ๐—ช๐—ถ๐˜๐—ต๐—ผ๐˜‚๐˜ ๐—Ÿ๐—ผ๐˜€๐—ถ๐—ป๐—ด ๐—œ๐—ป๐˜€๐—ถ๐—ด๐—ต๐˜๐˜€

๐—ช๐—ต๐—ฎ๐˜ ๐—˜๐˜…๐—ฎ๐—ฐ๐˜๐—น๐˜† ๐—œ๐˜€ ๐—ฃ๐—–๐—”?
โคท ๐—ฃ๐—–๐—” is a ๐—บ๐—ฎ๐˜๐—ต๐—ฒ๐—บ๐—ฎ๐˜๐—ถ๐—ฐ๐—ฎ๐—น ๐˜๐—ฒ๐—ฐ๐—ต๐—ป๐—ถ๐—พ๐˜‚๐—ฒ used to transform a ๐—ต๐—ถ๐—ด๐—ต-๐—ฑ๐—ถ๐—บ๐—ฒ๐—ป๐˜€๐—ถ๐—ผ๐—ป๐—ฎ๐—น dataset into fewer dimensions, while retaining as much ๐˜ƒ๐—ฎ๐—ฟ๐—ถ๐—ฎ๐—ฏ๐—ถ๐—น๐—ถ๐˜๐˜† (๐—ถ๐—ป๐—ณ๐—ผ๐—ฟ๐—บ๐—ฎ๐˜๐—ถ๐—ผ๐—ป) as possible.
โคท Think of it as โ€œ๐—ฐ๐—ผ๐—บ๐—ฝ๐—ฟ๐—ฒ๐˜€๐˜€๐—ถ๐—ป๐—ดโ€ data, similar to how we reduce the size of an image without losing too much detail.

๐—ช๐—ต๐˜† ๐—จ๐˜€๐—ฒ ๐—ฃ๐—–๐—” ๐—ถ๐—ป ๐—ฌ๐—ผ๐˜‚๐—ฟ ๐—ฃ๐—ฟ๐—ผ๐—ท๐—ฒ๐—ฐ๐˜๐˜€?
โคท ๐—ฆ๐—ถ๐—บ๐—ฝ๐—น๐—ถ๐—ณ๐˜† your data for ๐—ฒ๐—ฎ๐˜€๐—ถ๐—ฒ๐—ฟ ๐—ฎ๐—ป๐—ฎ๐—น๐˜†๐˜€๐—ถ๐˜€ and ๐—บ๐—ผ๐—ฑ๐—ฒ๐—น๐—ถ๐—ป๐—ด
โคท ๐—˜๐—ป๐—ต๐—ฎ๐—ป๐—ฐ๐—ฒ machine learning models by reducing ๐—ฐ๐—ผ๐—บ๐—ฝ๐˜‚๐˜๐—ฎ๐˜๐—ถ๐—ผ๐—ป๐—ฎ๐—น ๐—ฐ๐—ผ๐˜€๐˜
โคท ๐—ฉ๐—ถ๐˜€๐˜‚๐—ฎ๐—น๐—ถ๐˜‡๐—ฒ multi-dimensional data in 2๐—— or 3๐—— for insights
โคท ๐—™๐—ถ๐—น๐˜๐—ฒ๐—ฟ ๐—ผ๐˜‚๐˜ ๐—ป๐—ผ๐—ถ๐˜€๐—ฒ and uncover hidden patterns in your data

๐—ง๐—ต๐—ฒ ๐—ฃ๐—ผ๐˜„๐—ฒ๐—ฟ ๐—ผ๐—ณ ๐—ฃ๐—ฟ๐—ถ๐—ป๐—ฐ๐—ถ๐—ฝ๐—ฎ๐—น ๐—–๐—ผ๐—บ๐—ฝ๐—ผ๐—ป๐—ฒ๐—ป๐˜๐˜€
โคท The ๐—ณ๐—ถ๐—ฟ๐˜€๐˜ ๐—ฝ๐—ฟ๐—ถ๐—ป๐—ฐ๐—ถ๐—ฝ๐—ฎ๐—น ๐—ฐ๐—ผ๐—บ๐—ฝ๐—ผ๐—ป๐—ฒ๐—ป๐˜ is the direction in which the data varies the most.
โคท Each subsequent component represents the ๐—ป๐—ฒ๐˜…๐˜ ๐—ต๐—ถ๐—ด๐—ต๐—ฒ๐˜€๐˜ ๐—ฟ๐—ฎ๐˜๐—ฒ of variance, but is ๐—ผ๐—ฟ๐˜๐—ต๐—ผ๐—ด๐—ผ๐—ป๐—ฎ๐—น (๐˜‚๐—ป๐—ฐ๐—ผ๐—ฟ๐—ฟ๐—ฒ๐—น๐—ฎ๐˜๐—ฒ๐—ฑ) to the previous one.
โคท The challenge is selecting how many components to keep based on the ๐˜ƒ๐—ฎ๐—ฟ๐—ถ๐—ฎ๐—ป๐—ฐ๐—ฒ they explain.

๐—ฃ๐—ฟ๐—ฎ๐—ฐ๐˜๐—ถ๐—ฐ๐—ฎ๐—น ๐—˜๐˜…๐—ฎ๐—บ๐—ฝ๐—น๐—ฒ

1: ๐—–๐˜‚๐˜€๐˜๐—ผ๐—บ๐—ฒ๐—ฟ ๐—ฆ๐—ฒ๐—ด๐—บ๐—ฒ๐—ป๐˜๐—ฎ๐˜๐—ถ๐—ผ๐—ป
Imagine youโ€™re working on a project to ๐˜€๐—ฒ๐—ด๐—บ๐—ฒ๐—ป๐˜ customers for a marketing campaign, with data on spending habits, age, income, and location.
โคท Using ๐—ฃ๐—–๐—”, you can reduce these four variables into just ๐˜๐˜„๐—ผ ๐—ฝ๐—ฟ๐—ถ๐—ป๐—ฐ๐—ถ๐—ฝ๐—ฎ๐—น ๐—ฐ๐—ผ๐—บ๐—ฝ๐—ผ๐—ป๐—ฒ๐—ป๐˜๐˜€ that retain 90% of the variance.
โคท These two new components can then be used for ๐—ธ-๐—บ๐—ฒ๐—ฎ๐—ป๐˜€ clustering to identify distinct customer groups without dealing with the complexity of all the original variables.

๐—ง๐—ต๐—ฒ ๐—ฃ๐—–๐—” ๐—ฃ๐—ฟ๐—ผ๐—ฐ๐—ฒ๐˜€๐˜€ โ€” ๐—ฆ๐˜๐—ฒ๐—ฝ-๐—•๐˜†-๐—ฆ๐˜๐—ฒ๐—ฝ
โคท ๐—ฆ๐˜๐—ฒ๐—ฝ ๐Ÿญ: ๐——๐—ฎ๐˜๐—ฎ ๐—ฆ๐˜๐—ฎ๐—ป๐—ฑ๐—ฎ๐—ฟ๐—ฑ๐—ถ๐˜‡๐—ฎ๐˜๐—ถ๐—ผ๐—ป
Ensure your data is on the same scale (e.g., mean = 0, variance = 1).
โคท ๐—ฆ๐˜๐—ฒ๐—ฝ ๐Ÿฎ: ๐—–๐—ผ๐˜ƒ๐—ฎ๐—ฟ๐—ถ๐—ฎ๐—ป๐—ฐ๐—ฒ ๐— ๐—ฎ๐˜๐—ฟ๐—ถ๐˜…
Calculate how features are correlated.
โคท ๐—ฆ๐˜๐—ฒ๐—ฝ ๐Ÿฏ: ๐—˜๐—ถ๐—ด๐—ฒ๐—ป ๐——๐—ฒ๐—ฐ๐—ผ๐—บ๐—ฝ๐—ผ๐˜€๐—ถ๐˜๐—ถ๐—ผ๐—ป
Compute the eigenvectors and eigenvalues to determine the principal components.
โคท ๐—ฆ๐˜๐—ฒ๐—ฝ ๐Ÿฐ: ๐—ฆ๐—ฒ๐—น๐—ฒ๐—ฐ๐˜ ๐—–๐—ผ๐—บ๐—ฝ๐—ผ๐—ป๐—ฒ๐—ป๐˜๐˜€
Choose the top-k components based on the explained variance ratio.
โคท ๐—ฆ๐˜๐—ฒ๐—ฝ ๐Ÿฑ: ๐——๐—ฎ๐˜๐—ฎ ๐—ง๐—ฟ๐—ฎ๐—ป๐˜€๐—ณ๐—ผ๐—ฟ๐—บ๐—ฎ๐˜๐—ถ๐—ผ๐—ป
Transform your data onto the new ๐—ฃ๐—–๐—” space with fewer dimensions.

๐—ช๐—ต๐—ฒ๐—ป ๐—ก๐—ผ๐˜ ๐˜๐—ผ ๐—จ๐˜€๐—ฒ ๐—ฃ๐—–๐—”
โคท ๐—ฃ๐—–๐—” is not suitable when the dataset contains ๐—ป๐—ผ๐—ป-๐—น๐—ถ๐—ป๐—ฒ๐—ฎ๐—ฟ ๐—ฟ๐—ฒ๐—น๐—ฎ๐˜๐—ถ๐—ผ๐—ป๐˜€๐—ต๐—ถ๐—ฝ๐˜€ or ๐—ต๐—ถ๐—ด๐—ต๐—น๐˜† ๐˜€๐—ธ๐—ฒ๐˜„๐—ฒ๐—ฑ ๐—ฑ๐—ฎ๐˜๐—ฎ.
โคท For non-linear data, consider ๐—ง-๐—ฆ๐—ก๐—˜ or ๐—ฎ๐˜‚๐˜๐—ผ๐—ฒ๐—ป๐—ฐ๐—ผ๐—ฑ๐—ฒ๐—ฟ๐˜€ instead.

https://whatsapp.com/channel/0029VaC7Weq29753hpcggW2A ๐Ÿ“ฑ
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๐Ÿ“€ 55+ AI and Data Science Projects


๐Ÿ’ป Often you read all these articles, watch online courses, but until you do a practical project, start coding, and implement the concepts in practice, you don't learn anything.


๐Ÿ”ธ Here is a list of 55 projects in different categories:๐Ÿ‘‡


1โƒฃ Large language models ๐Ÿ”ธ Link

๐Ÿ”ข Fine-tuning LLMs ๐Ÿ”ธ Link

๐Ÿ”ข Time series data analysis ๐Ÿ”ธ Link

๐Ÿ”ข Computer Vision ๐Ÿ”ธ Link

๐Ÿ”ข Data Science ๐Ÿ”ธ Link

โž–โž–โž–โž–โž–
โช You can also access all of the above projects through the following GitHub repo: ๐Ÿ‘‡

โ”Œ
๐Ÿ“‚ AI Data Guided Projects
โ””
๐Ÿฑ GitHub-Repos

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A new interactive sentiment visualization project has been developed, featuring a dynamic smiley face that reflects sentiment analysis results in real time. Using a natural language processing model, the system evaluates input text and adjusts the smiley face expression accordingly:

๐Ÿ™‚ Positive sentiment

โ˜น๏ธ Negative sentiment

The visualization offers an intuitive and engaging way to observe sentiment dynamics as they happen.

๐Ÿ”— GitHub: https://lnkd.in/e_gk3hfe
๐Ÿ“ฐ Article: https://lnkd.in/e_baNJd2

#AI #SentimentAnalysis #DataVisualization #InteractiveDesign #NLP #MachineLearning #Python #GitHubProjects #TowardsDataScience

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This channels is for Programmers, Coders, Software Engineers.

0๏ธโƒฃ Python
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from SQL to pandas.pdf
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๐Ÿผ "Comparison Between SQL and pandas" โ€“ A Handy Reference Guide

โšก๏ธ As a data scientist, I often found myself switching back and forth between SQL and pandas during technical interviews. I was confident answering questions in SQL but sometimes struggled to translate the same logic into pandas โ€“ and vice versa.

๐Ÿ”ธ To bridge this gap, I created a concise booklet in the form of a comparison table. It maps SQL queries directly to their equivalent pandas implementations, making it easy to understand and switch between both tools.

โšก This reference guide has become an essential part of my interview prep. Before any interview, I quickly review it to ensure Iโ€™m ready to tackle data manipulation tasks using either SQL or pandas, depending on whatโ€™s required.

๐Ÿ“• Whether you're preparing for interviews or just want to solidify your understanding of both tools, this comparison guide is a great way to stay sharp and efficient.

#DataScience #SQL #pandas #InterviewPrep #Python #DataAnalysis #CareerGrowth #TechTips #Analytics

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๐ŸŸฃ AI Paper by Hand.pdf
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๐ŸŸฃ AI Paper by Hand โœ๏ธ

[1] ๐—ช๐—ต๐—ฎ๐˜ ๐— ๐—ฎ๐˜๐˜๐—ฒ๐—ฟ๐˜€ ๐—ถ๐—ป ๐—ง๐—ฟ๐—ฎ๐—ป๐˜€๐—ณ๐—ผ๐—ฟ๐—บ๐—ฒ๐—ฟ๐˜€? ๐—ก๐—ผ๐˜ ๐—”๐—น๐—น ๐—”๐˜๐˜๐—ฒ๐—ป๐˜๐—ถ๐—ผ๐—ป ๐—ถ๐˜€ ๐—ก๐—ฒ๐—ฒ๐—ฑ๐—ฒ๐—ฑ

[2] ๐—ฃ๐—ฟ๐—ฒ๐—ฑ๐—ถ๐—ฐ๐˜๐—ถ๐—ป๐—ด ๐—ณ๐—ฟ๐—ผ๐—บ ๐—ฆ๐˜๐—ฟ๐—ถ๐—ป๐—ด๐˜€: ๐—Ÿ๐—ฎ๐—ป๐—ด๐˜‚๐—ฎ๐—ด๐—ฒ ๐— ๐—ผ๐—ฑ๐—ฒ๐—น ๐—˜๐—บ๐—ฏ๐—ฒ๐—ฑ๐—ฑ๐—ถ๐—ป๐—ด๐˜€ ๐—ณ๐—ผ๐—ฟ ๐—•๐—ฎ๐˜†๐—ฒ๐˜€๐—ถ๐—ฎ๐—ป ๐—ข๐—ฝ๐˜๐—ถ๐—บ๐—ถ๐˜‡๐—ฎ๐˜๐—ถ๐—ผ๐—ป

[3] ๐— ๐—ข๐——๐—˜๐—Ÿ ๐—ฆ๐—ช๐—”๐—ฅ๐— ๐—ฆ: ๐—–๐—ผ๐—น๐—น๐—ฎ๐—ฏ๐—ผ๐—ฟ๐—ฎ๐˜๐—ถ๐˜ƒ๐—ฒ ๐—ฆ๐—ฒ๐—ฎ๐—ฟ๐—ฐ๐—ต ๐˜๐—ผ ๐—”๐—ฑ๐—ฎ๐—ฝ๐˜ ๐—Ÿ๐—Ÿ๐—  ๐—˜๐˜…๐—ฝ๐—ฒ๐—ฟ๐˜๐˜€ ๐˜ƒ๐—ถ๐—ฎ ๐—ฆ๐˜„๐—ฎ๐—ฟ๐—บ ๐—œ๐—ป๐˜๐—ฒ๐—น๐—น๐—ถ๐—ด๐—ฒ๐—ป๐—ฐ๐—ฒ

[4] ๐—ง๐—›๐—œ๐—ก๐—ž๐—œ๐—ก๐—š ๐—Ÿ๐—Ÿ๐— ๐—ฆ: ๐—š๐—ฒ๐—ป๐—ฒ๐—ฟ๐—ฎ๐—น ๐—œ๐—ป๐˜€๐˜๐—ฟ๐˜‚๐—ฐ๐˜๐—ถ๐—ผ๐—ป ๐—™๐—ผ๐—น๐—น๐—ผ๐˜„๐—ถ๐—ป๐—ด ๐˜„๐—ถ๐˜๐—ต ๐—ง๐—ต๐—ผ๐˜‚๐—ด๐—ต๐˜ ๐—š๐—ฒ๐—ป๐—ฒ๐—ฟ๐—ฎ๐˜๐—ถ๐—ผ๐—ป

[5] ๐—ข๐—ฝ๐—ฒ๐—ป๐—ฉ๐—Ÿ๐—”: ๐—”๐—ป ๐—ข๐—ฝ๐—ฒ๐—ป-๐—ฆ๐—ผ๐˜‚๐—ฟ๐—ฐ๐—ฒ ๐—ฉ๐—ถ๐˜€๐—ถ๐—ผ๐—ป-๐—Ÿ๐—ฎ๐—ป๐—ด๐˜‚๐—ฎ๐—ด๐—ฒ-๐—”๐—ฐ๐˜๐—ถ๐—ผ๐—ป ๐— ๐—ผ๐—ฑ๐—ฒ๐—น

[6] ๐—ฅ๐—ง-๐Ÿญ: ๐—ฅ๐—ผ๐—ฏ๐—ผ๐˜๐—ถ๐—ฐ๐˜€ ๐—ง๐—ฟ๐—ฎ๐—ป๐˜€๐—ณ๐—ผ๐—ฟ๐—บ๐—ฒ๐—ฟ ๐—ณ๐—ผ๐—ฟ ๐—ฅ๐—ฒ๐—ฎ๐—น-๐—ช๐—ผ๐—ฟ๐—น๐—ฑ ๐—–๐—ผ๐—ป๐˜๐—ฟ๐—ผ๐—น ๐—”๐˜ ๐—ฆ๐—ฐ๐—ฎ๐—น๐—ฒ

[7] ฯ€๐Ÿฌ: ๐—” ๐—ฉ๐—ถ๐˜€๐—ถ๐—ผ๐—ป-๐—Ÿ๐—ฎ๐—ป๐—ด๐˜‚๐—ฎ๐—ด๐—ฒ-๐—”๐—ฐ๐˜๐—ถ๐—ผ๐—ป ๐—™๐—น๐—ผ๐˜„ ๐— ๐—ผ๐—ฑ๐—ฒ๐—น ๐—ณ๐—ผ๐—ฟ ๐—š๐—ฒ๐—ป๐—ฒ๐—ฟ๐—ฎ๐—น ๐—ฅ๐—ผ๐—ฏ๐—ผ๐˜ ๐—–๐—ผ๐—ป๐˜๐—ฟ๐—ผ๐—น

[8] ๐—ฅ๐—ฒ๐˜๐—ฟ๐—ถ๐—ฒ๐˜ƒ๐—ฎ๐—น๐—”๐˜๐˜๐—ฒ๐—ป๐˜๐—ถ๐—ผ๐—ป: ๐—”๐—ฐ๐—ฐ๐—ฒ๐—น๐—ฒ๐—ฟ๐—ฎ๐˜๐—ถ๐—ป๐—ด ๐—Ÿ๐—ผ๐—ป๐—ด-๐—–๐—ผ๐—ป๐˜๐—ฒ๐˜…๐˜ ๐—Ÿ๐—Ÿ๐—  ๐—œ๐—ป๐—ณ๐—ฒ๐—ฟ๐—ฒ๐—ป๐—ฐ๐—ฒ ๐˜ƒ๐—ถ๐—ฎ ๐—ฉ๐—ฒ๐—ฐ๐˜๐—ผ๐—ฟ ๐—ฅ๐—ฒ๐˜๐—ฟ๐—ถ๐—ฒ๐˜ƒ๐—ฎ๐—น

[9] ๐—ฃ-๐—ฅ๐—”๐—š: ๐—ฃ๐—ฟ๐—ผ๐—ด๐—ฟ๐—ฒ๐˜€๐˜€๐—ถ๐˜ƒ๐—ฒ ๐—ฅ๐—ฒ๐˜๐—ฟ๐—ถ๐—ฒ๐˜ƒ๐—ฎ๐—น ๐—”๐˜‚๐—ด๐—บ๐—ฒ๐—ป๐˜๐—ฒ๐—ฑ ๐—š๐—ฒ๐—ป๐—ฒ๐—ฟ๐—ฎ๐˜๐—ถ๐—ผ๐—ป ๐—™๐—ผ๐—ฟ ๐—ฃ๐—น๐—ฎ๐—ป๐—ป๐—ถ๐—ป๐—ด ๐—ผ๐—ป ๐—˜๐—บ๐—ฏ๐—ผ๐—ฑ๐—ถ๐—ฒ๐—ฑ ๐—˜๐˜ƒ๐—ฒ๐—ฟ๐˜†๐—ฑ๐—ฎ๐˜† ๐—ง๐—ฎ๐˜€๐—ธ

[10] ๐—ฅ๐˜‚๐—”๐—š: ๐—Ÿ๐—ฒ๐—ฎ๐—ฟ๐—ป๐—ฒ๐—ฑ-๐—ฅ๐˜‚๐—น๐—ฒ-๐—”๐˜‚๐—ด๐—บ๐—ฒ๐—ป๐˜๐—ฒ๐—ฑ ๐—š๐—ฒ๐—ป๐—ฒ๐—ฟ๐—ฎ๐˜๐—ถ๐—ผ๐—ป ๐—™๐—ผ๐—ฟ ๐—Ÿ๐—ฎ๐—ฟ๐—ด๐—ฒ ๐—Ÿ๐—ฎ๐—ป๐—ด๐˜‚๐—ฎ๐—ด๐—ฒ ๐— ๐—ผ๐—ฑ๐—ฒ๐—น๐˜€

[11] ๐—ข๐—ป ๐˜๐—ต๐—ฒ ๐—ฆ๐˜‚๐—ฟ๐—ฝ๐—ฟ๐—ถ๐˜€๐—ถ๐—ป๐—ด ๐—˜๐—ณ๐—ณ๐—ฒ๐—ฐ๐˜๐—ถ๐˜ƒ๐—ฒ๐—ป๐—ฒ๐˜€๐˜€ ๐—ผ๐—ณ ๐—”๐˜๐˜๐—ฒ๐—ป๐˜๐—ถ๐—ผ๐—ป ๐—ง๐—ฟ๐—ฎ๐—ป๐˜€๐—ณ๐—ฒ๐—ฟ ๐—ณ๐—ผ๐—ฟ ๐—ฉ๐—ถ๐˜€๐—ถ๐—ผ๐—ป ๐—ง๐—ฟ๐—ฎ๐—ป๐˜€๐—ณ๐—ผ๐—ฟ๐—บ๐—ฒ๐—ฟ๐˜€

[12] ๐— ๐—ถ๐˜…๐˜๐˜‚๐—ฟ๐—ฒ-๐—ผ๐—ณ-๐—ง๐—ฟ๐—ฎ๐—ป๐˜€๐—ณ๐—ผ๐—ฟ๐—บ๐—ฒ๐—ฟ๐˜€: ๐—” ๐—ฆ๐—ฝ๐—ฎ๐—ฟ๐˜€๐—ฒ ๐—ฎ๐—ป๐—ฑ ๐—ฆ๐—ฐ๐—ฎ๐—น๐—ฎ๐—ฏ๐—น๐—ฒ ๐—”๐—ฟ๐—ฐ๐—ต๐—ถ๐˜๐—ฒ๐—ฐ๐˜๐˜‚๐—ฟ๐—ฒ ๐—ณ๐—ผ๐—ฟ ๐— ๐˜‚๐—น๐˜๐—ถ-๐— ๐—ผ๐—ฑ๐—ฎ๐—น ๐—™๐—ผ๐˜‚๐—ป๐—ฑ๐—ฎ๐˜๐—ถ๐—ผ๐—ป ๐— ๐—ผ๐—ฑ๐—ฒ๐—น๐˜€

[13]-[14] ๐—˜๐—ฑ๐—ถ๐—ณ๐˜† ๐Ÿฏ๐——: ๐—ฆ๐—ฐ๐—ฎ๐—น๐—ฎ๐—ฏ๐—น๐—ฒ ๐—›๐—ถ๐—ด๐—ต-๐—ค๐˜‚๐—ฎ๐—น๐—ถ๐˜๐˜† ๐Ÿฏ๐—— ๐—”๐˜€๐˜€๐—ฒ๐˜ ๐—š๐—ฒ๐—ป๐—ฒ๐—ฟ๐—ฎ๐˜๐—ถ๐—ผ๐—ป

[15] ๐—•๐˜†๐˜๐—ฒ ๐—Ÿ๐—ฎ๐˜๐—ฒ๐—ป๐˜ ๐—ง๐—ฟ๐—ฎ๐—ป๐˜€๐—ณ๐—ผ๐—ฟ๐—บ๐—ฒ๐—ฟ: ๐—ฃ๐—ฎ๐˜๐—ฐ๐—ต๐—ฒ๐˜€ ๐—ฆ๐—ฐ๐—ฎ๐—น๐—ฒ ๐—•๐—ฒ๐˜๐˜๐—ฒ๐—ฟ ๐—ง๐—ต๐—ฎ๐—ป ๐—ง๐—ผ๐—ธ๐—ฒ๐—ป๐˜€

[16]-[18] ๐——๐—ฒ๐—ฒ๐—ฝ๐—ฆ๐—ฒ๐—ฒ๐—ธ-๐—ฉ๐Ÿฏ (๐—ฃ๐—ฎ๐—ฟ๐˜ ๐Ÿญ-๐Ÿฏ)

[19] ๐—ง๐—ฟ๐—ฎ๐—ป๐˜€๐—ณ๐—ผ๐—ฟ๐—บ๐—ฒ๐—ฟ๐˜€ ๐˜„๐—ถ๐˜๐—ต๐—ผ๐˜‚๐˜ ๐—ก๐—ผ๐—ฟ๐—บ๐—ฎ๐—น๐—ถ๐˜‡๐—ฎ๐˜๐—ถ๐—ผ๐—ป

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Scientific Visualization: Python + Matplotlib

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