Every now and then we follow a text book in mathematics. Let us assume it’s a high school algebra book, the classic Hall and Knight. So, we are looking at the middle term break factorization. So, there are a lot of examples; just a few manipulations in the figures else the skeleton of the problems is more or less same. So, this excellent observation can actually be put to a wonderful use by software designers and programmers to design automated problem generation in Mathematics. The type or variety of problems shall span from basic linear equations, quadratic problems to matrix manipulations, interpolations and so on. The basic objective of the algorithm is to ease the efforts from the shoulders of teachers and academicians in preparing question papers. Moreover, we have put in a lot of thought regarding the diversity and difficulty level of generated problems in details using collaborative algorithms and machine learning.

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.
9/5/2015Prepared by: Abhishek Dey, Developer, Cloud Architect. 2

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.
9/5/2015Prepared by: Abhishek Dey, Developer, Cloud Architect. 3

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 ? 
9/5/2015Prepared by: Abhishek Dey, Developer, Cloud Architect. 4

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
9/5/2015Prepared by: Abhishek Dey, Developer, Cloud Architect. 5

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.
9/5/2015Prepared by: Abhishek Dey, Developer, Cloud Architect. 6

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.
9/5/2015Prepared by: Abhishek Dey, Developer, Cloud Architect. 7

8. Architecture of the back end
Backend
Database
ProcessingQueueWrites data
Contacts tracker
We areTrackers!
We keep track of
jobs
9/5/2015Prepared by: Abhishek Dey, Developer, Cloud Architect. 8

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.
9/5/2015Prepared by: Abhishek Dey, Developer, Cloud Architect. 9

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
9/5/2015Prepared by: Abhishek Dey, Developer, Cloud Architect. 10

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
9/5/2015Prepared by: Abhishek Dey, Developer, Cloud Architect. 11

12. What’s the point?
We hate these
situations!
We want a
solution.
Maybe unique.

9/5/2015Prepared by: Abhishek Dey, Developer, Cloud Architect. 12

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.
9/5/2015Prepared by: Abhishek Dey, Developer, Cloud Architect. 13

14. To all the teachers,
on Teacher’s Day
ThankYou.
uriosity
ommitment
ommunityC