
Priority Queue is an extension of queue with following properties:

- Every item has a priority associated with it.
- An element with high priority is dequeued before an element with low priority.
- If two elements have the same priority, they are served according to their order in the queue.

A typical priority queue supports following operations:

- `insert(item, priority)`: Inserts an item with given priority.
- `getHighestPriority()`: Returns the highest priority item.
- `deleteHighestPriority()`: Removes the highest priority item.

Applications of Priority Queue:

- CPU Scheduling
- Graph algorithms like Dijkstra’s shortest path algorithm, Prim’s Minimum Spanning Tree, etc
- All queue applications where priority is involved.
- Data Compression (Huffman codes)
- Find the largest M items in a stream of N items.

Ways to implement Priority Queue:

- Arrays - Insertion and Deletion is expensive in order to maintain the priority.
- LinkedList -> Same as array, but deletion is fast.
- Binary Heap -> Best

## Binary Heap (Min Heap or Max Heap)

- Based on the `idea = 10` of Complete Binary Tree.
- Binary Tree: Empty or Nodes to left and right binary tree.
- Complete Binary Tree: Perfectly Balanced, except for the bottom level and the bottom level has all keys as left as possible.
  - Perfectly Balanced, except for Level 3
  - Height of a Complete Binary Tree of N node is Log N.
    In the shown tree, there are 9 nodes ==> Log 9 = Log 3^2 = 2 Log 3. (3 Levels)

![Binary Tree Levels](/images/dsa/tree-levels.png 'Binary Tree Levels')

Implementation: Array representation of the heap ordered complete binary tree.

Heap Ordered Binary Tree:

- Keys in nodes.
- Parent's key is greater than children's keys. This is important.

Properties of Binary Heap:

- Largest key is arr[1], which is the root of the binary tree.
- Parent of node at 'k' index is at k/2 index. (It's integer divide. No floats)
- Children of a node 'k' are at index '2k' and '2k + 1', **given we start indexing from 1 instead of 0.**

Consider this array:

```js
index       0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
arr[index] [_, T, S, R, P, N, O, A, E, I,  H, G]
```

![Heap Example](/images/dsa/heap-example.png 'Heap Example')

### What's the parent of H & G?

Parent of node at 'k' is at k/2. Here k = 10(H), so parent will be at 10/2 = 5. Element at index 5 is N, which is correct!  
So, we don't need actual tree to represent these data structures. Array indices are sufficient.

Time complexity for building a Binary Heap is O(N). Read more about the complexity [here](https://stackoverflow.com/questions/9755721/how-can-building-a-heap-be-on-time-complexity)

## Implementation

```ts
type Comparator<T> = (a: T, b: T) => number

class Heap<T> {
  items: T[]
  comparator: Comparator<T>

  constructor(list: T[], comparator: Comparator<T>) {
    this.items = list || []
    this.comparator = comparator
    this.buildHeap()
  }

  buildHeap(): void {
    for (let i = Math.floor(this.size() / 2) - 1; i >= 0; i--) {
      this.moveDown(i)
    }
  }

  moveDown(curIdx: number): void {
    const lastIndex = this.size() - 1
    const items = this.items
    while (this.leftChild(curIdx) <= lastIndex) {
      let i = this.leftChild(curIdx)

      // if i is not the last element -> compare i with i+1
      // if i was the last element, i+1 would give us index out of bound!
      if (i < lastIndex && this.comparator(items[i], items[i + 1]) < 0) {
        i++
      }

      if (this.comparator(items[i], items[curIdx]) < 0) {
        break
      }

      this.exchange(curIdx, i)
      curIdx = i
    }
  }

  moveUp(curIdx: number): void {
    while (curIdx > 0) {
      let parent = this.parent(curIdx)
      if (this.comparator(this.items[curIdx], this.items[parent]) < 0) break
      this.exchange(parent, curIdx)
      curIdx = parent
    }
  }

  offer(value: T) {
    this.items.push(value)
    this.moveUp(this.size() - 1)
  }

  poll(): T | null {
    if (this.size() === 0) return null

    const item = this.items[0]
    const last = this.items.pop()

    if (this.size() && last) {
      this.items[0] = last
      this.moveDown(0)
    }

    return item
  }

  leftChild(parent: number): number {
    return 2 * parent + 1
  }

  rightChild(parent: number): number {
    return 2 * parent + 2
  }

  parent(child: number): number {
    return Math.floor((child - 1) / 2)
  }

  peek(): T {
    return this.items[0]
  }

  size(): number {
    return this.items.length
  }

  isEmpty(): boolean {
    return this.size() === 0
  }

  exchange(i: number, j: number): void {
    let temp = this.items[i]
    this.items[i] = this.items[j]
    this.items[j] = temp
  }
}
```


Implementing Heap in TypeScript

Linear Algebra


A few things I want to accomplish in 2023:

### Top Level Goals

- [ ] Solve 150 Leetcode Questions
- [ ] Learn Linear Algebra
- [ ] Learn Calculus
- [ ] ML courses
  - [ ] [Intro to Machine Learning by Kaggle](https://www.kaggle.com/learn/intro-to-machine-learning)
  - [ ] [Intermediate Machine Learning by Kaggle](https://www.kaggle.com/learn/intermediate-machine-learning)
  - [ ] [Pandas](https://www.kaggle.com/learn/pandas)
  - [ ] [Data Viz.](https://www.kaggle.com/learn/data-visualization)
- [ ] Hands ML challenges
  - [ ] [Titanic](https://www.kaggle.com/competitions/titanic)
  - [ ] [House Pricing](https://www.kaggle.com/competitions/house-prices-advanced-regression-techniques)
  - [ ] [Predict Future Sales](https://www.kaggle.com/competitions/competitive-data-science-predict-future-sales)
  - [ ] [Digit Recognizer](https://www.kaggle.com/competitions/digit-recognizer)
  - [ ] [Spaceshipt Titanic](https://www.kaggle.com/competitions/spaceship-titanic)
- [ ] Read 5 books
  - [ ] [The Book of proof](http://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf)
  - [ ] [How to prove it](https://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/0521675995)
  - [ ] [Coffee can investing](https://www.amazon.in/Coffee-Can-Investing-Stupendous-Wealth/dp/067009045X)
  - [ ] [The unsual billionaire](https://www.amazon.in/gp/product/B06XXZ6C6S)
  - [ ] [Introducing Game Theory: A Graphic Guide](https://www.amazon.in/Introducing-Game-Theory-Graphic-Guide-ebook/dp/B01J4P6L90)

### Rough Timelines

Mar-Apr:

- Leetcode and Job

Mar-Apr-May:

- Linear Algebra
- The Book of proof

Jun-Jul-Aug:

- Calculus
- ML courses

Sept-Oct-Nov-Dec:

- ML Courses
- Projects


2023 Goals


Some of the courses I want to take:

### Economics and Finance

- [ ] [Economics of Money and Banking by Perry G Mehrling](https://in.coursera.org/learn/money-banking)
- [ ] [Finacial Markets by Robert Shiller](https://www.youtube.com/playlist?list=PL8FB14A2200B87185)
- [ ] [Finance Theory 1 by Andrew Lo](https://www.youtube.com/watch?v=HdHlfiOAJyE&list=PLUl4u3cNGP63B2lDhyKOsImI7FjCf6eDW)
- [ ] [Financial Theory by John Geanakoplos](https://www.youtube.com/playlist?list=PLEDC55106E0BA18FC)
- [ ] [Introduction to Microeconomics](https://mru.org/courses/principles-economics-microeconomics/introduction-microeconomics)
- [ ] [Principles of Economics: Macroeconomics](https://mru.org/principles-economics-macroeconomics-0)
- [ ] [William Ackman: Everything You Need to Know About Finance and Investing](https://www.youtube.com/watch?v=WEDIj9JBTC8)
- [ ] [Become a Master of Finance with Harvard Professor Mihir Desai](https://www.youtube.com/watch?v=oSGld-eY7BM)
- [ ] [Intro to Economics: Crash Course](https://www.youtube.com/watch?v=3ez10ADR_gM&list=PLhYj2OiS_cFmaUckvZv8dn1KtKhLSSTL8)
- [ ] [Microeconomics- Everything You Need to Know](https://www.youtube.com/watch?v=1UxA6JzoT-4)
- [ ] [MIT: Principles of Microeconomics](https://www.youtube.com/watch?v=_OkTw766oCs&list=PLUl4u3cNGP62oJSoqb4Rf-vZMGUBe59G-&index=1)

### Mathematics

- [ ] [Mathematics for Machine Learning Specialization](https://www.coursera.org/specializations/mathematics-machine-learning?)
- [ ] [Linear Algebra for Machine Learning](https://www.youtube.com/watch?v=Qc19jQWHdL0&list=PLRDl2inPrWQW1QSWhBU0ki-jq_uElkh2a&index=1)
- [ ] [Linear Algebra for Machine Learning](https://www.youtube.com/watch?v=T73ldK46JqE&list=PLiiljHvN6z1_o1ztXTKWPrShrMrBLo5P3&index=1)
- [ ] [Linear Algebra for beginner](https://www.youtube.com/watch?v=kZwSqZuBMGg)
- [ ] [Linear Algebra from beginner to experts](https://www.youtube.com/watch?v=t5ckUuSsWe4)
- [ ] [Linear Algebra Refresher Course](https://www.udacity.com/course/linear-algebra-refresher-course--ud953)
- [ ] [Eigen vectors and Eigen values](https://www.udacity.com/course/eigenvectors-and-eigenvalues--ud104)
- [ ] [Multivariate calculus](https://www.youtube.com/watch?v=cWZLPv4ZJhE&list=PLiiljHvN6z193BBzS0Ln8NnqQmzimTW23)
- [ ] [Calculus for beginners](https://www.youtube.com/watch?v=8stueNPVl-I)
- [ ] [Visual Information Theory](https://colah.github.io/posts/2015-09-Visual-Information/)

### Statistics & Probability

- [ ] [Statistics and Probability](https://www.youtube.com/watch?v=sbbYntt5CJk)
- [ ] [Statistics for beginner](https://www.youtube.com/watch?v=hjZJIVWHnPE)
- [ ] [Teach me Statistics in half an hour](https://www.youtube.com/watch?v=kyjlxsLW1Is)

### Machine Learning

- [ ] [Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow - Aurélien Géron](https://www.amazon.in/gp/product/9355421982/)
- [ ] [Intro to Machine Learning by Kaggle](https://www.kaggle.com/learn/intro-to-machine-learning)
- [ ] [Intermediate Machine Learning by Kaggle](https://www.kaggle.com/learn/intermediate-machine-learning)
- [ ] [Introduction to Machine Learning by Google](https://developers.google.com/machine-learning/crash-course/ml-intro)
- [ ] [Introduction to Machine Learning Problem Framing](https://developers.google.com/machine-learning/problem-framing)
- [ ] [Deep Learning Book](https://www.deeplearningbook.org/)
- [ ] [Neural Networks: Zero to Hero by Andrew Karpathy](https://karpathy.ai/zero-to-hero.html)
- [ ] [Articial Intelligence for Trading](https://www.udacity.com/course/ai-for-trading--nd880)
- [ ] [Introduction to Machine Learning Course](https://www.udacity.com/course/intro-to-machine-learning--ud120)
- [ ] [AWS Machine learning foundation course](https://www.udacity.com/course/aws-machine-learning-foundations--ud065)
- [ ] [Train and evaluate regression models](https://learn.microsoft.com/en-gb/training/modules/train-evaluate-regression-models/3-exercise-model)
- [ ] [Machine learning system design - Stanford](https://stanford-cs329s.github.io/syllabus.html)
- [ ] [Learn from ML experts at Google](https://ai.google/education/)
- [ ] [More resources from Twitter thread](https://twitter.com/marktenenholtz/status/1522184346324459520)
- [ ] [Neural Network From Scratch](https://sirupsen.com/napkin/neural-net)
- [ ] [Machine Learning - Tom M. Mitchell](https://www.amazon.in/Machine-Learning-Tom-M-Mitchell/dp/1259096955)

### General

- [ ] [Human Behavioral Biology](https://www.youtube.com/watch?v=NNnIGh9g6fA&list=PL848F2368C90DDC3D&index=1)
- [ ] [Model Thinking by Scott E. Page](https://www.coursera.org/learn/model-thinking)
- [ ] [Modern World](https://www.coursera.org/learn/modern-world)
- [ ] [The Modern World, Part Two: Global History since 1910](https://www.coursera.org/learn/modern-world-2)
- [ ] [Game theory 101](https://www.youtube.com/playlist?list=PLKI1h_nAkaQoDzI4xDIXzx6U2ergFmedo)


Courses & Videos


- [ ] [The Model Thinker by Scott E. Page](https://www.amazon.in/Model-Thinker-Scott-Page/dp/0465094627)
- [ ] [Investonomy](https://www.amazon.in/Investonomy-Stock-Market-Guide-Makes/dp/0143455044)
- [ ] [Learn to earn](https://www.amazon.in/Learn-Earn-Beginners-Investing-Business/dp/0684811634)
- [ ] [The Education of a value investor](https://www.amazon.in/Education-Value-Investor-Transformative-Enlightenment/dp/1137278811)
- [ ] [The Age of Cryptocurrency](https://www.amazon.in/gp/product/1250081556/)
- [ ] [The Manual of ideas](https://www.amazon.in/Manual-Ideas-Framework-Finding-Investments/dp/1118083652)
- [ ] [Five rules of successful stock investing](https://www.amazon.in/Five-Rules-Successful-Stock-Investing/dp/0471686174)
- [ ] [Tuesday with Morrie](https://www.amazon.in/Tuesdays-Morrie-young-greatest-lesson/dp/0751527378)
- [ ] [Coffee can investing](https://www.amazon.in/Coffee-Can-Investing-Stupendous-Wealth/dp/067009045X)
- [ ] [Diamond in the dust](https://www.amazon.in/gp/product/B09BRDMD85)
- [ ] [The unsual billionaire](https://www.amazon.in/gp/product/B06XXZ6C6S)
- [ ] [Introducing Game Theory: A Graphic Guide](https://www.amazon.in/Introducing-Game-Theory-Graphic-Guide-ebook/dp/B01J4P6L90)


Bookshelf


## Latex Symbols

Frequently used:

- \frac{d}{dr} \pi r^2 $\longrightarrow$ $\frac{d}{dr} \pi r^2$
- \int*{a}^{b} x^2 \\,dx $\longrightarrow$ $\int*{a}^{b} x^2 \,dx$
- \sum*{n=1}^\infty \frac{1}{n^s} $\longrightarrow$ $\sum*{n=1}^\infty \frac{1}{n^s}$
- \frac{1}{2} \rho v^2 S C_L $\longrightarrow$ $\frac{1}{2} \rho v^2 S C_L$
- \mathbf{R} $\longrightarrow$ $\mathbf{R}$
- \mathbb{R}^(m x n) $\longrightarrow$ $\mathbb{R}^{m \times n}$

Refer to these sheets for more:

- [1](https://kapeli.com/cheat_sheets/LaTeX_Math_Symbols.docset/Contents/Resources/Documents/index)
- [2](http://tug.ctan.org/info/undergradmath/undergradmath.pdf)

![Math Notation](/images/maths/math-notation.png "Math Notation")
![Set Notation](/images/maths/set-notation.png "Set Notation")
![Vector Notation](/images/maths/vector-notation.png "Vector Notation")
![Complex Numbers Notation](/images/maths/complex-number-notation.png "Complex Numbers Notation")
![Vector Space Notation](/images/maths/vector-space-notation.png "Vector Space Notation")
![Matrices and Matrix Operations Notation](/images/maths/matrix-and-operation-notation.png "Matrices and Matrix Operations Notation")
![Notation for linear transformations](/images/maths/notation-for-linear-transformations.png "Notation for linear transformations")
![Matrix decompositions](/images/maths/matrix-decomposition-notation.png "Matrix decompositions")
![Abstract vector space notation](/images/maths/abstract-vector-space-notation.png "Abstract vector space notation")


Mathematical Symbols & Notations


> Think in terms of X-Rays and Time-lapse - betterexplained.com

## Derivative

$$
\frac{d}{dx} y
$$

This is X-Ray, which means split the whole into (possibly different) parts along the _x-axis_

Think of a circle: if you split the circle into smaller circles so that each sub-circle has some smaller radius than the original one then it's called X-Ray vision.

X-Ray is not a concept in Calculas. It's simply used just to describe it.

## Integral

$$
\int_{r=0}^{r} 2 \pi r \,dr
$$

This is Time-Lapse, which means accumulate (possibly different) steps along the _r direction_


Calculus


### Generic:

- [Book of Proof: Richard Hammack](http://www.people.vcu.edu/~rhammack/BookOfProof/)
- [How to Prove It: A Structured Approach, 2nd Edition: Daniel J. Velleman](https://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/0521675995)
- [Introduction to Mathematical Philosophy: Bertrand Russell](https://www.amazon.com/Introduction-Mathematical-Philosophy-Bertrand-Russell/dp/1684221447)
- [How to develop your intuition for math: BetterExplained](https://betterexplained.com/articles/developing-your-intuition-for-math/)
- [3Blue1Brown: Lockdown math on several topics](https://www.youtube.com/watch?v=ppWPuXsnf1Q&list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev)

### Linear Algebra:

- [Essence of Linear Algebra: 3Blue1Brown](https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab)
- [No Bullshit Guide To Linear Algebra - Ivan Savov](https://www.amazon.in/gp/product/0992001021)
- [Practical Linear Algebra for Data Science - Mike Cohen](https://www.amazon.in/gp/product/9355422180)
- [Learn Linear Algebra Intuitively: BetterExplaied](https://betterexplained.com/articles/linear-algebra-guide/)
- [Linear Algebra Done Right 3rd ed. 2015 Edition: Sheldon Axler](https://www.amazon.com/Linear-Algebra-Right-Undergraduate-Mathematics/dp/3319110799)
- [No bullshit guide to linear algebra 2nd Edition: Ivan Savov](https://www.amazon.com/No-bullshit-guide-linear-algebra/dp/0992001021)
- [Coding the Matrix: Linear Algebra through Applications to Computer Science 1st Edition: Philip N. Klein](https://www.amazon.com/Coding-Matrix-Algebra-Applications-Computer/dp/0615880991)
- [Linear Algebra and Optimization for Machine Learning: Charu C. Aggarwal](https://www.amazon.com/Linear-Algebra-Optimization-Machine-Learning/dp/3030403432)
- [Algebra: PatrickJMT](http://patrickjmt.com/#algebra)
- [Intermediate Algebra: Professor Leonard](https://youtube.com/playlist?list=PLC292123722B1B450)
- [Linear Algebra: PatrickJMT](http://patrickjmt.com/#linear-algebra)
- [Vector and Dot Product: Freya Holmér](https://www.youtube.com/watch?v=MOYiVLEnhrw)
- [Space and Cross Product: Freya Holmér](https://www.youtube.com/watch?v=XiwEyopOMqg)
- [Art of Problem Solving](https://artofproblemsolving.com/store/list/aops-curriculum#problem-solving)
- [Interactive Linear Algebra](http://immersivemath.com/ila/index.html)
- [Wild Linear Algebra](https://www.youtube.com/watch?v=yAb12PWrhV0&list=PLIljB45xT85BhzJ-oWNug1YtUjfWp1qAp&index=1)
- [Linear Algebra](https://www.youtube.com/watch?v=I04GHpKc-WQ&list=PLlXfTHzgMRULWJYthculb2QWEiZOkwTSU)
- Introduction to Linear Algebra 5th Edition: Gilbert Strang
  - [Book: 4th Edition](https://www.amazon.com/Introduction-Linear-Algebra-Fourth-Gilbert/dp/0980232716)
  - [Book: 5th Edition](https://www.amazon.com/Introduction-Linear-Algebra-Gilbert-Strang/dp/0980232775/)
  - [Videos](https://www.youtube.com/watch?v=ZK3O402wf1c&list=PL49CF3715CB9EF31D&index=1)

### Trigonometry:

- [Plane Trigonometry: S L Loney](https://www.amazon.in/PLANE-TRIGONOMETRY-Part-1-S-Loney/dp/9351761754)
- [Intuitive Guide to Angles, Degrees and Radians: Better Explained](https://betterexplained.com/articles/intuitive-guide-to-angles-degrees-and-radians/)
- [Intuitive Trigonometry: BetterExplained](https://betterexplained.com/articles/intuitive-trigonometry/)
- [Trigonometry: Freya Holmér](https://www.youtube.com/watch?v=1NLekEd770w)
- [Interpolation & Velocity: Freya Holmér](https://www.youtube.com/watch?v=-Ii3MrJFBkQ)
- [Trigonometry course for beginners](https://www.youtube.com/watch?v=5zi5eG5Ui-Y)

### Calculus:

- [Essence of Calculus: 3Blue1Brown](https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr)
- [Calculus - Thomas & Finney](http://www.sufwan.com/wp-content/uploads/CalculusAndAnalyticalGeometry/Calculus-Book-Thomas-Finney.pdf)
- [Learn Calculus Intuitively: Better Explained](https://betterexplained.com/calculus/lesson-1/)
- [Limits: Better Explained](https://betterexplained.com/articles/an-intuitive-introduction-to-limits/)
- [Calculus: An Intuitive and Physical Approach: Morris Kline](https://www.amazon.com/Calculus-Intuitive-Physical-Approach-Mathematics/dp/0486404536)
- [Differential Equations with Applications and Historical Notes, 2nd Edition: George F. Simmons](https://www.amazon.com/Differential-Applications-Historical-International-Mathematics/dp/0070575401)
- [Calculus and Analytical Geometry 6th Edition: Louis Leithold](https://www.amazon.com/Calculus-Analytical-Geometry-Louis-Leithold/dp/0060441070)
- [Calculus, 4th edition: Michael Spivak](https://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098918)
- [MIT Calculus Revisited: Single Variable Calculus](https://www.youtube.com/watch?v=MFRWDuduuSw&list=PL4buDdUD7fvhVAlLpfF2lIhWmRd6Rd7Wj&index=1)
- [Multivariable Calculus: 3Blue1Brown ](https://www.youtube.com/watch?v=TrcCbdWwCBc&list=PLSQl0a2vh4HC5feHa6Rc5c0wbRTx56nF7&index=1)
- [Differential Equation: Paul's notes](https://tutorial.math.lamar.edu/classes/de/de.aspx)
- [Calculus: PatrickJMT](http://patrickjmt.com/#calculus)
- [Pre-Calculus: Professor Leonard](https://www.youtube.com/watch?v=FkUEsP9efFg&list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&index=2)
- [Calculus 1: Professor Leonard](https://www.youtube.com/playlist?list=PLF797E961509B4EB5)
- [Calculus 2: Professor Leonard](https://www.youtube.com/watch?v=H9eCT6f_Ftw&list=PLDesaqWTN6EQ2J4vgsN1HyBeRADEh4Cw-)
- [Calculus 3: Professor Leonard](https://www.youtube.com/watch?v=tGVnBAHLApA&list=PLDesaqWTN6ESk16YRmzuJ8f6-rnuy0Ry7)
- Calculus Made Easy Revised, Updated, Expanded Edition: Silvanus P. Thompson
  - [Book](https://www.amazon.com/Calculus-Made-Easy-Silvanus-Thompson/dp/0312185480)
  - [Website](https://calculusmadeeasy.org/)

### Probability & Statistics:

- [The Elements of Statistical Learning - Jerome Friedman](https://www.amazon.in/Elements-Statistical-Learning-Prediction-Statistics/dp/0387848576/)
- [Random Phenomena: Fundamentals of Probability and Statistics for Engineers 1st Edition: Babatunde A. Ogunnaike](https://www.amazon.com/Random-Phenomena-Fundamentals-Probability-Statistics/dp/1420044974)
- [The Drunkard's Walk: How Randomness Rules Our Lives: Leonard Mlodinow](https://www.amazon.com/Drunkards-Walk-Randomness-Rules-Lives/dp/0307275175)
- [MIT: Introduction to Probability](https://www.youtube.com/playlist?list=PLUl4u3cNGP60hI9ATjSFgLZpbNJ7myAg6)
- [O'REILLY - Practical Statistics For Data Scientist - Peter Bruce](https://www.amazon.in/gp/product/8194435005/)

### Discrete Mathematics:

- [Discrete Mathematics: Introduction to Mathematical Reasoning 1st Edition: Susanna S. Epp](https://www.amazon.com/Discrete-Mathematics-Introduction-Mathematical-Reasoning/dp/0495826170)
- [Mathematics for Computer Science: MIT OCW](https://www.youtube.com/watch?v=L3LMbpZIKhQ&list=PLB7540DEDD482705B&index=1)


Mathematics Resources



Unlike Grid, Flex box is 1-Dimensional.

By default:
1. The Main Axis is from Left -> Right and Cross Axis is Top -> Bottom.
2. Items try to fit themselves in a single row. It means they don't wrap themselves onto the next line even when there's no space; they'll shrink to minimum possible width. It doesn't work even if you specify larger width. To wrap them onto the next line, you need to specify `flex-wrap`.  

**justify-content**: distribute space between items along the Main Axis. 

**Note**: not just in-between items.

Default value is: flex-start 
Other options: space-between | center | space-around | flex-end

![Intro](/images/flexbox/intro.png "Intro of Flex Box")
![Intro](/images/flexbox/row.png "Intro of Flex Box")
![Intro](/images/flexbox/row-reverse.png "Intro of Flex Box")
![Intro](/images/flexbox/column.png "Intro of Flex Box")
![Intro](/images/flexbox/column-reverse.png "Intro of Flex Box")