The document presents a new approach to automatic problem generation in mathematical analysis, detailing the limitations of traditional machine analysis and proposing a faster algorithm based on the fundamental law of arithmetic. It outlines a distributed processing model for generating unique mathematical questions and emphasizes the use of machine learning and user feedback to define problem difficulty. The aim is to create a user-friendly interface for selecting question quantity and difficulty, while contributing to a community-driven educational platform.

1. Automatic Problem
Generation
A new approach to Mathematical analysis
Presented by: Abhishek Dey. Developer. Architect.

2. What is a problem?
▪ Take a typical example (Algebra):
𝑎𝑥2 + 𝑏𝑥 + 𝑐 = 0 is a quadratic equation. Resolve the factors.
Approach:
1. We multiply a*c and resolve the common factors.
2. We manipulate them and try to rearrange equation to satisfy constraint b.
3. 𝑎𝑥2 + 𝑏′ 𝑥 + 𝑏 − 𝑏′ 𝑥 + 𝑐 = 0 where b’ is a constant.
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3. Human Analysis Vs. Machine Analysis
Factorize a*c.
I. assume expr=a*c
II. take a suitable integer x and divide expr/x
III. if remainder is divisible by x, continue
(expr-x)/x else, check for a new divisor y
(expr-x)/y.
IV. repeat unless expr reduces to a prime
number or 1.
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4. Computer’s Algorithm:
▪ Has to start from 2 and continue checking up to a*c-1 times.
▪ Iterator 𝑖 ≔ 2 to 𝑖 ≔ 𝑒𝑥𝑝𝑟 − 1
– If 𝑒𝑥𝑝𝑟%𝑖 ≔ 0, then
▪ 𝑒𝑥𝑝𝑟 ≔ 𝑒𝑥𝑝𝑟/𝑖
– Else
▪ 𝑖 + +
▪ Do you think this is smart ? 
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5. A better approach
▪ Fundamental Law of Arithmetic:
– Every composite number can be expressed as a product of primes.
▪ This makes the algorithm faster and smarter.
Number Number of Divisors
Prime 2
Square of a prime 3
Cube of a prime 4
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6. Problem with Machines
▪ They generate random figures.
– Can you solve 48885𝑥2
+ 3287𝑥 + 95670 = 0 ?
– Probably. But not in a limited time.
▪ The generated problem may not have a unique solution.
▪ Some problems such as Matrix Chain multiplication, Bellman Ford,
Dijkstra may require a lot of processing power.
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7. Where there is will, there is a unique
solution
▪ Processing Queue:
– We use a distributed processing model.
– Some problems from our end, others from customer’s end.
– We maintain a processing queue.
– A worker role that keeps record of all the distributed tasks
going on.
Example:
Say, we have a customer X who wants 10 questions on
quadratic equations.The server supplies 5 of them and
the remaining is generated in his system and backed up
in our server.
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8. Architecture of the back end
Backend
Database
ProcessingQueueWrites data
Contacts tracker
We areTrackers!
We keep track of
jobs
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9. Determining a unique solution
▪ We form aTree.
▪ Trace all paths that can be followed.
▪ If we reach a wrong node, we trace
back using Backtracking.
▪ Finally the correct path is determined.
▪ If the tree is too complex we use
Union-Find algorithm.
▪ This also helps us to know the
difficulty level of a problem.
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10. Another problem has come up!
▪ When a user chooses a level of difficulty for
the generated problems, what do we mean
by EASY or HARD?
▪ EASY is a relative term.
▪ So, we employ 2 things:
– A Machine Learning mechanism based on
sentiment analysis.
– Feedback from live customers.
– What is MACHINE LEARNING?? :O
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11. Achieved Throughput
0
5000000
10000000
15000000
20000000
25000000
30000000
35000000
40000000
500 1000 10,000 1,00,000 10,00,000 20,00,000
NO.OFQUESTIONS
NO. OF DEVICES
NO. OF DEVICES
No. of devices
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12. What’s the point?
We hate these
situations!
We want a
solution.
Maybe unique.

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13. The UI and UX:
▪ Users will be offered:
– Choose number of questions.
– Choose difficulty level of questions.
– If not satisfied with response, option to discard
question by just a slide.
– The experience is sleek and hassle free.
▪ What we shall get:
– We are Opensource. Not just FREE.
– Entire profits from advertisements.
– You contribute your processing power. (a little bit.)
– Build a platform for teachers.
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14. To all the teachers,
on Teacher’s Day
ThankYou.
uriosity
ommitment
ommunityC