Thursday, April 24, 2025

BIS601 Full Stack Development - Model Questions

 

  1. How do you declare variables and initialize them in javascript? Give examples for each data type.

// 1️⃣ String (Text)

let name = "John Doe"; // Double quotes

let message = 'Hello, World!'; // Single quotes

let greeting = `Welcome, ${name}`; // Template literal

console.log(name, message, greeting);


// 2️⃣ Number (Integer & Float)

let age = 25; // Integer

let price = 99.99; // Floating-point

console.log(age, price);


// 3️⃣ Boolean (True/False)

let isLoggedIn = true;

let hasPermission = false;

console.log(isLoggedIn, hasPermission);


// 4️⃣ Undefined (No value assigned)

let user;

console.log(user); // Output: undefined


// 5️⃣ Null (Explicitly no value)

let emptyValue = null;

console.log(emptyValue); // Output: null


// 6️⃣ Object (Key-Value Pairs)

let person = {

    name: "Alice",

    age: 30,

    isStudent: false

};

console.log(person);


// 7️⃣ Array (List of Values)

let colors = ["Red", "Green", "Blue"];

let numbers = [10, 20, 30, 40];

console.log(colors, numbers);


// 8️⃣ Symbol (Unique Identifier)

let id = Symbol("userID");

console.log(id);


// 9️⃣ BigInt (For large numbers beyond Number.MAX_SAFE_INTEGER)

let bigNumber = 123456789012345678901234567890n;

console.log(bigNumber);


// 🔹 var, let, and const Usage

var x = 10;  // Function-scoped, can be redeclared

let y = 20;  // Block-scoped, cannot be redeclared

const z = 30; // Constant, cannot be reassigned

console.log(x, y, z);



  1. Give examples of the following in JS

    1. Instructions 

console.log("Hello, World!"); // Instruction to print a message

let sum = 5 + 3; // Instruction to add numbers and store the result



  1. Comment

// This is a single-line comment

let x = 10; // This variable stores the number 10


/* 

   This is a multi-line comment.

   It can span multiple lines.

*/

let y = 20;


  1. Statements

let a = 10; // Variable declaration statement

a = a + 5; // Assignment statement

console.log(a); // Function call statement

if (a > 10) { console.log("A is greater than 10"); } // Conditional statement


  1. Variable declaration

var oldVar = "I am declared using var"; // Function-scoped (not recommended)

let age = 25; // Block-scoped (preferred for variables that change)

const PI = 3.1416; // Constant value (cannot be reassigned)



  1. What do you mean by dynamically typed and interpreted languages? 

Write a recursive function in js to find the factorial of a number and display the result on the console.

function factorial(n) {

    if (n === 0 || n === 1) {

        return 1;

    }

    return n * factorial(n - 1);

}


const num = 5; // Change this to any number you want to test

console.log(`Factorial of ${num} is: ${factorial(num)}`);


  1. Write a js script to display the numbers 0 to 9 except a number entered via prompt. Preferably use a do while loop.


const skipNumber = parseInt(prompt("Enter a number to skip   

                          (0-9):"), 10);

let i = 0;

do {

    if (i !== skipNumber) {

        console.log(i);

    }

    i++;

} while (i < 10);



  1. a) Write a JavaScript program that displays the largest integer among two integers

b) Write a JavaScript conditional statement to find the sign of the product of three numbers. Display an alert box with the specified sign

Input: 3,-9 , 6                  Output: -ve sign

const num1 = parseInt(prompt("Enter the first integer:"), 10);

const num2 = parseInt(prompt("Enter the second integer:"), 10);


if (num1 > num2) {

    console.log(`The larger number is: ${num1}`);

} else if (num2 > num1) {

    console.log(`The larger number is: ${num2}`);

} else {

    console.log("Both numbers are equal.");

}

Prgm2:

const num1 = parseFloat(prompt("Enter the first number:"));

const num2 = parseFloat(prompt("Enter the second number:"));

const num3 = parseFloat(prompt("Enter the third number:"));


const product = num1 * num2 * num3;


if (product > 0) {

    alert("The sign of the product is: +ve");

} else if (product < 0) {

    alert("The sign of the product is: -ve");

} else {

    alert("The product is zero (0).");

}



  1. a) Write a JavaScript conditional statement to find the largest of five numbers. Display an alert box to show the results.

b) Write a JavaScript for loop that iterates from 0 to 15. For each iteration, it checks if the current number is odd or even, and displays a message on the screen.

Sample Output :"0 is even"  "1 is odd"  "2 is even"

const num1 = parseFloat(prompt("Enter the first number:"));

const num2 = parseFloat(prompt("Enter the second number:"));

const num3 = parseFloat(prompt("Enter the third number:"));

const num4 = parseFloat(prompt("Enter the fourth number:"));

const num5 = parseFloat(prompt("Enter the fifth number:"));

const largest = Math.max(num1, num2, num3, num4, num5);

alert(`The largest number is: ${largest}`);

for (let i = 0; i <= 15; i++) {

    if (i % 2 === 0) {

        console.log(`${i} is even`);

    } else {

        console.log(`${i} is odd`);

    }

}

  1. Write a JavaScript program to construct the following pattern, using a nested for loop.

*  

* *  

* * *  

* * * *  

* * * * * 

let pattern = "";


for (let i = 1; i <= 5; i++) {

    for (let j = 1; j <= i; j++) {

        pattern += "* ";

    }

    pattern += "\n";

}


console.log(pattern);



  1. Write a JavaScript program to compute the greatest common divisor (GCD) of two positive integers.

function gcd(a, b) {

    while (b !== 0) {

        let temp = b;

        b = a % b;

        a = temp;

    }

    return a;

}


const num1 = parseInt(prompt("Enter the first positive integer:"), 10);

const num2 = parseInt(prompt("Enter the second positive integer:"), 10);


if (num1 > 0 && num2 > 0) {

    alert(`The GCD of ${num1} and ${num2} is: ${gcd(num1, num2)}`);

} else {

    alert("Please enter valid positive integers.");

}



  1. Write a JavaScript program to sum 3 and 5 multiples under 1000.

let sum = 0;


for (let i = 0; i < 1000; i++) {

    if (i % 3 === 0 || i % 5 === 0) {

        sum += i;

    }

}


console.log(`The sum of all multiples of 3 and 5 below 1000 is: ${sum}`);

  1. Reversing a Number with JavaScript While Loop.

function reverseNumber(num) {

    let reversed = 0;

 while (num !== 0) {

        let digit = num % 10; // Get the last digit

        reversed = reversed * 10 + digit; // Append digit to reversed number

        num = Math.floor(num / 10); // Remove the last digit

    }

    return reversed;

}

const num = parseInt(prompt("Enter a number to reverse:"), 10);

alert(`The reversed number is: ${reverseNumber(num)}`);

  1. Finding the Largest Digit in a Number Using a While Loop.

function largestDigit(num) {

    num = Math.abs(num); // Ensure the number is positive

    let maxDigit = 0;

    while (num !== 0) {

        let digit = num % 10; // Extract the last digit

        if (digit > maxDigit) {

            maxDigit = digit; // Update maxDigit if current digit is larger

        }

        num = Math.floor(num / 10); // Remove the last digit

    }

    return maxDigit;

}

const num = parseInt(prompt("Enter a number:"), 10);

alert(`The largest digit in ${num} is: ${largestDigit(num)}`);

  1. Checking Prime Numbers Using While Loop in JavaScript.

function isPrime(num) {

    if (num < 2) return false; // 0 and 1 are not prime numbers

    let i = 2;

    while (i <= Math.sqrt(num)) {

        if (num % i === 0) {

            return false; // If divisible, not a prime number

        }

        i++;

    }

    return true;

}

const num = parseInt(prompt("Enter a number:"), 10);


if (isPrime(num)) {

    alert(`${num} is a prime number.`);

} else {

    alert(`${num} is not a prime number.`);

}


  1. Write a JavaScript program to list the properties of a JavaScript object.

Sample object:
var student = {name : "Ram Rahim", sclass : "VI", rollno : 12 };
Sample Output: name, sclass, rollno

var student = { name: "Ram Rahim", sclass: "VI", rollno: 12 };

console.log(Object.keys(student).join(", "));

  1. Write a JavaScript program to delete the roll-no property from the following object. Also print the object before or after deleting the property.

Sample object:
var student = { name : "ram rahim", sclass : "VI", rollno : 12 };

var student = { name: "Ram Rahim", sclass: "VI", rollno: 12 };

console.log("Before deletion:", student);

delete student.rollno;

console.log("After deletion:", student);


  1. Write a JavaScript program to get the volume of a cylindrical with four decimal places using object classes.

Volume of a cylinder : V = πr2h

where r is the radius and h is the height of the cylinder.

class Cylinder {

    constructor(radius, height) {

        this.radius = radius;

        this.height = height;

    }

    getVolume() {

        let volume = Math.PI * Math.pow(this.radius, 2) * this.height;

        return volume.toFixed(4); // Round to 4 decimal places

    }

}

const radius = parseFloat(prompt("Enter the radius of the cylinder:"));

const height = parseFloat(prompt("Enter the height of the cylinder:"));

const cylinder = new Cylinder(radius, height);

alert(`The volume of the cylinder is: ${cylinder.getVolume()}`);


  1. Write a JavaScript program to calculate circle area and perimeter.

Note : Create two methods to calculate the area and perimeter. The radius of the circle will be supplied by the user.

class Circle {

    constructor(radius) {

        this.radius = radius;

    }

    // Method to calculate the area

    getArea() {

        return (Math.PI * Math.pow(this.radius, 2)).toFixed(2);

    }

    // Method to calculate the perimeter (circumference)

    getPerimeter() {

        return (2 * Math.PI * this.radius).toFixed(2);

    }

}

// Get user input for radius

const radius = parseFloat(prompt("Enter the radius of the circle:"));

if (!isNaN(radius) && radius > 0) {

    const circle = new Circle(radius);

    alert(`Circle Area: ${circle.getArea()} \nCircle Perimeter: ${circle.getPerimeter()}`);

} else {

    alert("Please enter a valid positive number for the radius.");

}

  1. For the following script what problem might be encountered in the addHx function?

<script>

  function createElementAsChild(parent, tag){

            let tagInstance = document.createElement(tag)

            parent.appendChild(tagInstance)

            return tagInstance

        }

        function addHx(parent, tag, content){

            tagInstance = createElementAsChild(parent, tag)

            tagInstance.textContent = content

            return tagInstance

        }

  let body = document.body

  let h3Tag =  addHx(body, "h3")

</script>

How does javascript handle errors?

FInal fixed code:

function createElementAsChild(parent, tag) {

    let tagInstance = document.createElement(tag);

    parent.appendChild(tagInstance);

    return tagInstance;

}


function addHx(parent, tag, content = "") { // Default value prevents "undefined"

    let tagInstance = createElementAsChild(parent, tag);

    tagInstance.textContent = content;

    return tagInstance;

}


let body = document.body;

let h3Tag = addHx(body, "h3", "Hello, this is H3!"); // Proper function call



  1. Write a js script to add the following in the body of an html document using dom manipulation by invoking functions document.createElement() and parent.appendChild().

<body>

     <h1> Hello World</h1>

     <h2>I am SuperMan</h2>

    <h3>I am SpiderNam</h3>

</body>


// Function to create and append elements

function addHeading(tag, text) {

    let heading = document.createElement(tag); // Create the element (h1, h2, h3)

    heading.textContent = text; // Set text content

    document.body.appendChild(heading); // Append to body

}



// Adding the elements dynamically

addHeading("h1", "Hello World");

addHeading("h2", "I am SuperMan");

addHeading("h3", "I am SpiderMan");



  1. What does the following code do?

<div>

        <span title="Window Title123" id="hi">Hello</span>

        <span id="bye">Bye</span>

    </div>

    <script>

        let div = document.querySelector("div")

        let hiSpan = document.querySelector("#hi")

        let byeSpan = document.querySelector("#bye")

        console.log(hiSpan.getAttribute("title"))

   </script>

Add a new attribute and remove an existing attribute for the hiSpan.

let div = document.querySelector("div");

let hiSpan = document.querySelector("#hi");

let byeSpan = document.querySelector("#bye");


console.log(hiSpan.getAttribute("title")); // Logs: "Window Title123"


// Add a new attribute

hiSpan.setAttribute("data-info", "newData");


// Remove the existing "title" attribute

hiSpan.removeAttribute("title");


// Check the changes

console.log(hiSpan.getAttribute("data-info")); // Logs: "newData"

console.log(hiSpan.getAttribute("title")); // Logs: null (because it's removed)



  1. Explain the following methods of selecting elements:

document.getElementById()

document.getElementsByName()

document.getElementsByTagName()

document.getElementsByClassName()

document.querySelector()

document.querySelectorAll() 

by giving a single html page and querying its elements by these methods.


<!DOCTYPE html>

<html lang="en">

<head>

    <meta charset="UTF-8">

    <meta name="viewport" content="width=device-width, initial-scale=1.0">

    <title>DOM Selection Example</title>

</head>

<body>


    <h1 id="main-title">Welcome to JavaScript DOM</h1>

    

    <p class="description">This is a paragraph inside the body.</p>

    <p class="description">Another paragraph with the same class.</p>


    <input type="text" name="username" value="John Doe">

    <input type="text" name="email" value="john@example.com">


    <div>

        <span class="info">Span inside div</span>

    </div>


    <ul>

        <li>Item 1</li>

        <li>Item 2</li>

        <li>Item 3</li>

    </ul>


    <script>

        // 1️⃣ document.getElementById("id")

        let title = document.getElementById("main-title");

        console.log("getElementById:", title.textContent);


        // 2️⃣ document.getElementsByName("name")

        let inputs = document.getElementsByName("username");

        console.log("getElementsByName:", inputs[0].value);


        // 3️⃣ document.getElementsByTagName("tagname")

        let paragraphs = document.getElementsByTagName("p");

        console.log("getElementsByTagName:", paragraphs[0].textContent);


        // 4️⃣ document.getElementsByClassName("classname")

        let descriptions = document.getElementsByClassName("description");

        console.log("getElementsByClassName:", descriptions[1].textContent);


        // 5️⃣ document.querySelector("selector")

        let firstListItem = document.querySelector("ul li");

        console.log("querySelector:", firstListItem.textContent);


        // 6️⃣ document.querySelectorAll("selector")

        let allListItems = document.querySelectorAll("ul li");

        allListItems.forEach(item => console.log("querySelectorAll:", item.textContent));

    </script>


</body>

</html>



Wednesday, February 26, 2025

VTU Phd Entrance Test - Jan 2025- Ver B


First page


Second Page


Third Page



                                                            Fourth Page



Fifth Page



Sixth Page



Seventh Page


Eight Page



Nineth Page



Tenth Page


Eleventh Page




Answer Key:










Sunday, November 19, 2017

Re-Engineering the Internet for Real Net Neutrality

"Internet needs not just regulation but also accurate and efficient metering of traffic to make it cost inefficient for piracy/human rights violators and hackers. Let charges for every packet going around in the internet be made. Many corporations will have to close down what with excessive charges for their automatic updates. Internet is heavily tilted in favor of the corporations. We(consumers) pay for viewing the ads(data costs). We have to bear all expenses no matter the benefiting party."

This was my comment in one of the sites where net neutrality was being discussed. In traditional transactions the benefiting party pays for the goods and services. In the internet it is always the user who pays no matter what he does with it. A model for charging for services where the real user pays and the real provider of service gets the money is needed.

Many users on the internet generate content and they are never credited for the data or talent they exhibit. Be it bloggers or You tube channels. A massive reorganization of the internet where charges for the network traffic are made based on the duration or volume of traffic carried could be tried. Every packet that goes around the internet should potentially be charged some money to someone just as a car pays for the toll on the roads.


Uniqueness and provenance should be the only guiding factors for people to lay claim to copyrights. Data compression alone will not reduce bandwidth requirements from network traffic and radical new ways of metering connections which is inclusive of people left out of the internet should be made to bridge the digital divide.

Internet is turning out to be a mega scam where mega corporations with ad servers and SEO companies are having a field day at the cost of the talent/copyright holder.

Your comments are welcome!

Sunday, April 2, 2017

Numerical Methods Problems

Some numerical methods problems from B S Grewal...

Regula - falsi
1) Find a real root of the equation x3-2x-5=0 by the method of false position correct to three decimal places.
2) Find the root of the equation cos x=xex using regular-falsi method correct to four decimal places.
3) Find the real root of the equation x log 10 x = 1.2 by regula-falsi method correct upto four decimal places.
4) Use the method of false position, to find the fourth root of 32 correct upto three decimal places.
5) Using regula-falsi method, find the real root of the following equations correct to three decimal places:
i) xex=2                 ii) cos x=3x-1      iii) xex=sinx    iv) x tanx=-1            v) 2x-logx=7       vi) 3x+sinx=ex
6) Find the fourth root of 12 correct to three decimal places by interpolation method(regula falsi)
7) Locate the root of f(x) = x10 -1=0 between 0 and 1.3 using method of false position.
Newton – Raphson
1) Find the positive root of x4-x=10 correct to three decimal places using newton-raphson method.
2) Find by newton’s method, the real root of the equation 3x=cosx+1 correct to four decimal places.
3) Using Newton’s iterative method, find the real root of x log 10 x = 1.2 correct to five decimal places.
4) Find by newton-raphson method, a root of the following equations correct upto 3 decimal places.
i) x3-3x+1=0     ii) x3-2x-5=0      iii) x3-5x+3=0       iv) 3x3-9x2+8=0
5) Using newton’s iterative method, find a root of the following equations correct to 4 decimal places:
i) x4+x3-7x2-x+5=0 which lies between 2 and 3.
ii) x5 – 5 x2 +3=0
6) Find the negative root of equation x3 -21x +3500=0 correct to 2 decimal places by newton’s method.
7) Using Newton-Raphson method, find a root of the following equations correct to 3 decimal places:
i) x2+4sinx=0
ii) x sinx+cosx=0
iii) ex=x3+cos25x which is near 4.5

iv) x log 10 x=12.34 start with x0=4.5
v) cosx = x ex
vi) 10x+x-4=0
8) use newton’s method to find the smallest root of the equation ex sinx=1 to four decimal places.
9) Develop an algorithm using N.R method, to find the fourth root of a positive number N and hence find .(fourth root of 32).

10) evaluate the following(correct to 3 decimal places) by using newton-raphson method.
i) 1/18                   ii) 1/ (square root of 15)             iii) (28)-1/4

11) State and explain the newton-raphson method to find the roots of a differentiable equation.


Gauss Elimination Method:
1) Apply the gauss elimination method to solve the equations x+4y-z=-5; x+y-6z=-12; 3x-y-z=4
2)Solve 10x-7y+3z+5u=6; -6x+8y-z-4u=5; 3x+y+4y+11u=2; 5x-9y-2z+4u=7 by gauss elimination.
3) Using gauss elimination method, solve the equations x+2y+3z-u=10, 2x+3y-3z-u=1, 2x-y+2z+3u=7, 3x+2y-4z+3u=2.
4) Solve the following equations by gauss elimination method:
i) x + y + z=9; 2x - 3y + 4z = 13; 3x + 4y + 5z = 40
ii) 2x + 2y + z = 12; 3x + 2y + 2z = 8; 5x + 10y -8z =10
iii) 2x – y + 3z = 9; x + y + z = 6; x – y + z=2
iv) 2x1 + 4x2 + x3 = 3; 3x1 + 2x2 – 2x3= -2; x1 – x2 + x3 = 6
v) 5x1 + x2 + x3 + x4 = 4; x1 + 7x2 + x3 + x4 = 12; x1 + x2 + 6x3 + x4 = -5; x1 + x2 + x3 + 4x4= -6

(Dekha daya gauss ne ek aur coefficient eliminate kar diya)

Gauss-jordan method:
1) Apply Gauss-jordan method to solve the equations
 x + y + z=9; 2x - 3y + 4z = 13; 3x + 4y + 5z = 40
2) Solve the equations 10x-7y+3z+5u=6;
                                                -6x+8y-z-4u=5;
                                                3x+y+4z+11u=2;
                                                5x-9y-2z+4u=7

3) solve the following equations by Gauss-Jordan Method:
i) 2x+5y+7z=52; 2x+y-z=0; x+y+z=9
ii) 2x – 3y +z=-1; x +4y +5z=25; 3x-4y+z=2
iii) x + y+ z=9; 2x+y-z=0; 2x+5y+7z=52
iv) x + 3y + 3z=16; x + 4y + 3z=18; x + 3y + 4z=19
v) 2x1+x2+5x3+x4=5; x1+x2-3x3+4x4=-1
    3x1+6x2-2x3+x4=8; 2x1+2x2+2x3-3x4=2

LU decomposition:
1) Solve the following equations by factorization method:
i) 2x+3y+z=9; x+2y+3z=6; 3x+y+2z=8
ii) 10x+y+z=12; 2x+10y+z=13; 2x+2y+10z=14
iii) 10x+y+2z=13; 3x+10y+z=14; 2x+3y+10z=15
iv) 2x1-x2+x3=-1; 2x2-x3+x4=1; x1+2x3-x4=-1; x1+x2+2x4=3

Iterative methods:
Jacobi’s Iteration:
1) Solve by Jacobi’s iteration method, the equations
20x+y-2z=17;
3x+20y-z=-18;
2x-3y+20z=25
2) Solve by jacobi’s iteration method, the equations 10x + y – z=11.19
                                                                                                       x+10y+z=28.08;
                                                                                                      -x+y+10z=35.61
3) Solve the equations:
10x1-2x2-x3-x4=3;
-2x1+10x2-x3-x4=15;
-x1-x2+10x3-2x4=27;
-x1-x2-2x3+10x4=-9

4) Solve by jacobi’s method, the equations: 5x-y+z=10;
                                                                                     2x+4y=12;
                                                                                     x+y+5z=-1 starting with the solution{2,3,0}

5) Solve by jacobi’s method the equations:
13x + 5y-3z+u=18;
2x+12y+z-4u=13;
x-4y+10z+u=29;
2x+y-3z+9u=31;

Gauss-Seidel Method:
1) Apply Gauss-Seidel iteration method to solve the equations 20x+y-2z=17
3x+20y-z=-18; 2x-3y+20z=25

2) Solve the equations 27x+6y-z=85;
                                                x+y+54z=110;
                                                6x+15y+2z=72;

3) Apply Gauss-Seidel iteration method to solve the equations:
10x1-2x2-x3-x4=3;
-2x1+10x2-x3-x4=15;
-x1-x2+10x3+2x4=27;
-x1-x2-2x3+10x4=-9

4) Solve the following equations by Gauss-seidel method:
i) 2x+y+6z=9; 8x+3y+2z=13; x+5y+z=7
ii) 28x+4y-z=32; x+3y+10z=24; 2x+17y+4z=35;
iii) 10x+y+z=12; 2x+10y+z=13; 2x+2y+10z=14;
iv) 7x1+52x2+13x3=104; 83x1+11x2-4x3=95; 3x1+8x2+29x3=71

v) 3x1-0.1x2-0.2x3=7.85; 0.1x1+7x2-0.3x3=-19.3; 0.3x1-0.2x2+10x3=71.4

Saturday, April 1, 2017

A Mathematician's Lament

A Mathematician’s Lament
by Paul Lockhart
A musician wakes from a terrible nightmare.  In his dream he finds himself in a society where music education has been made mandatory.  “We are helping our students become more competitive in an increasingly sound-filled world.”  Educators, school systems, and the state are put in charge of this vital project.  Studies are commissioned, committees are formed, and decisions are made— all without the advice or participation of a single working musician or composer.
Since musicians are known to set down their ideas in the form of sheet music, these curious black dots and lines must constitute the “language of music.”  It is imperative that students become fluent in this language if they are to attain any degree of musical competence; indeed, it would be ludicrous to expect a child to sing a song or play an instrument without having a thorough grounding in music notation and theory.  Playing and listening to music, let alone composing an original piece, are considered very advanced topics and are generally put off until college, and more often graduate school. 
As for the primary and secondary schools, their mission is to train students to use this language— to jiggle symbols around according to a fixed set of rules:  “Music class is where we take out our staff paper, our teacher puts some notes on the board, and we copy them or transpose them into a different key.  We have to make sure to get the clefs and key signatures right, and our teacher is very picky about making sure we fill in our quarter-notes completely.
One time we had a chromatic scale problem and I did it right, but the teacher gave me no credit because I had the stems pointing the wrong way.”  
In their wisdom, educators soon realize that even very young children can be given this kind of musical instruction.  In fact it is considered quite shameful if one’s third-grader hasn’t completely memorized his circle of fifths.  “I’ll have to get my son a music tutor.  He simply won’t apply himself to his music homework.  He says it’s boring.  He just sits there staring out the window, humming tunes to himself and making up silly songs.”
In the higher grades the pressure is really on.  After all, the students must be prepared for the standardized tests and college admissions exams.  Students must take courses in Scales and Modes, Meter, Harmony, and Counterpoint.  “It’s a lot for them to learn, but later in college when they finally get to hear all this stuff, they’ll really appreciate all the work they did in high school.”  Of course, not many students actually go on to concentrate in music, so only a few will ever get to hear the sounds that the black dots represent.  Nevertheless, it is important that every member of society be able to recognize a modulation or a fugal passage, regardless of the fact that they will never hear one.  “To tell you the truth, most students just aren’t very good at music.
They are bored in class, their skills are terrible, and their homework is barely legible.  Most of them couldn’t care less about how important music is in today’s world; they just want to take the minimum number of music courses and be done with it.  I guess there are just music people and non-music people.  I had this one kid, though, man was she sensational!  Her sheets were impeccable— every note in the right place, perfect calligraphy, sharps, flats, just beautiful. She’s going to make one hell of a musician someday.”

Waking up in a cold sweat, the musician realizes, gratefully, that it was all just a crazy dream.  “Of course!” he reassures himself, “No society would ever reduce such a beautiful and meaningful art form to something so mindless and trivial; no culture could be so cruel to its children as to deprive them of such a natural, satisfying means of human expression.  How absurd!”  

Meanwhile, on the other side of town, a painter has just awakened from a similar nightmare…

I was surprised to find myself in a regular school classroom— no easels, no tubes of paint.  “Oh we don’t actually apply paint until high school,” I was told by the students.  “In seventh grade we mostly study colors and applicators.”  They showed me a worksheet.  On one side were swatches of color with blank spaces next to them.  They were told to write in the names.  “I like painting,” one of them remarked, “they tell me what to do and I do it.  It’s easy!” 
After class I spoke with the teacher.  “So your students don’t actually do any painting?” I asked.  “Well, next year they take Pre-Paint-by-Numbers.  That prepares them for the main Paint-by-Numbers sequence in high school.  So they’ll get to use what they’ve learned here and apply it to real-life painting situations— dipping the brush into paint, wiping it off, stuff like that.
Of course we track our students by ability.  The really excellent painters— the ones who know their colors and brushes backwards and forwards— they get to the actual painting a little sooner, and some of them even take the Advanced Placement classes for college credit.  But mostly we’re just trying to give these kids a good foundation in what painting is all about, so when they get out there in the real world and paint their kitchen they don’t make a total mess of it.”

“Um, these high school classes you mentioned…”

“You mean Paint-by-Numbers?  We’re seeing much higher enrollments lately.  I think it’s mostly coming from parents wanting to make sure their kid gets into a good college.  Nothing looks better than Advanced Paint-by-Numbers on a high school transcript.”looks better than Advanced Paint-by-Numbers on a high school transcript.”

“Why do colleges care if you can fill in numbered regions with the corresponding color?”

“Oh, well, you know, it shows clear-headed logical thinking.  And of course if a student is planning to major in one of the visual sciences, like fashion or interior decorating, then it’s really a good idea to get your painting requirements out of the way in high school.”
“I see.  And when do students get to paint freely, on a blank canvas?”
“You sound like one of my professors!  They were always going on about expressing yourself and your feelings and things like that—really way-out-there abstract stuff.  I’ve got a degree in Painting myself, but I’ve never really worked much with blank canvasses.  I just use the Paint-by-Numbers kits supplied by the school board.”


Sadly, our present system of mathematics education is precisely this kind of nightmare.  In fact, if I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done— I simply wouldn’t have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education.