Statement of Purpose
I have been interested in mathematics and recently won gold honour for securing a rank among the top 5 percentile in International Youth Math Challenge, 2019. In high school, however, I was more interested in making funny questions which used to make even my teachers smile once they figured out the answers. This innate urge towards mathematical thinking made me switch my major from Material Science and Engineering to Economic Sciences. This decision was a turning point of my life because it introduced me to game theory and eventually led me to become a finalist in NC Ray Paper Presentation Competition, 2019 for my work ‘Grammar Acquisition Game’. Thus my long term objective molded into researching behavioural and experimental game theory.
Game Theory has a tendency to slither into astronomically different fields, ranging from mathematics to biology, and also an immense potential to mark its significance. In economics, while game theory has had an impact in understanding and theoretically modelling behaviour, experimental studies on decision making and economic behaviour has also changed how game theory used to be perceived. The research at UCL has produced interesting propositions about game theory and its applicability. The works such as ‘Behavioral Economics and the Atheoretical Style’ and ‘Coordination under limited depth of reasoning’ deal with concepts which I find very intriguing. Also the workshops and seminars organised at UCL provide immense scope for learning. So considering the opportunities and exposures University College London provides the exact environment required for me to grow and pursue an exciting career in research.
The combination of a major in Economic Sciences and a minor in Cognitive Science enabled me to understand different perspectives of decision making and learning in strategic environment. This understanding has motivated me to work at the intersection of the two fields. In my undergraduate project, ‘Investigating Reinforcement learning through Evolutionary Game Theory’ I determined the evolutionarily stable strategy for learning the type of an opponent in a finitely repeated prisoner’s dilemma. The reinforcement learning strategies were Bush-Mosteller model and Temporal Difference Learning Model. I found that Temporal Difference Learning model was the evolutionarily stable strategy, primarily due to myopic nature of Bush-Mosteller model. This project taught me how to model situations through game theoretic perspective. Moreover, I noticed that the likelihood of choice of action learnt through reinforcement learning and the proportion of population opting an action subject to replicator dynamics, follow different perspectives of a similar idea.
In ‘The Game of Adjustment’ I determined a subjective optimal point between two extremes of a dimension of adjustment. In psychology, adjustment is the process by which one achieves harmony with oneself and the environment through changes in their behaviour and there are six dimensions of adjustment each with their extremes. The motivation was to show that an individual can display behaviour comprising of different extremes rather than strictly adhering to the one they have been characterised as, depending on their environment. I verified the same for tolerance using game theory. Tolerance, one of the dimensions of adjustment, has two extremes one being indiscriminate acceptance of self and others and the other extreme rejection. That is, in a game-theoretic setting with available actions being acceptance and rejection, subjectively a mixed strategy can be an optimal solution and the individual can display acceptance with some non zero probability in a given environment.
In ‘Grammar Acquisition Game’ I modeled grammar learning using game theory. The Universal Grammar hypothesis postulates that the set of structural features of speech and language is finite, thus there can be a finite number of grammars. A learner will receive greater communication success if it uses those features which are being used in its environment. So the grammars which are similar to the grammar being used in the environment should have a higher likelihood of being taught than a dissimilar grammar. Thus the grammar being used in the environment must have greatest fitness, so a learner must select the evolutionarily stable grammar. I accounted for limited memory and processing by limiting the number grammars processed at a time. Now since the number of grammars is finite and the learner selects the grammar with highest fitness it will reach at the correct grammar. This model accounts for the fact that children in early stages can use incorrect grammar but eventually learn the correct one. This work made me the finalist in NC Ray Paper Presentation Competition, a platform for undergraduate students to showcase and test their ideas. The prevalent trend among my peers is to opt for non academic jobs so I faced extreme social pressure against opting a research career but this accomplishment encouraged me to overcome this hurdle.
I volunteered to be the academic mentor for mathematics in my first year as an undergraduate. My responsibilities included taking remedial classes, doubt clearing sessions and one on one tutoring for the course ‘Linear Algebra Ordinary Differential Equation’ and some subtopics of the course ‘Calculus’. After my tenure as an academic mentor I took an internship as content developer with Xprep, for which I was required to write original mathematics questions for high school students. In the course of my dual degree I gained interdisciplinary experience and being from a technological institute I have a strong mathematical background. I also have hands on experience and theoretical background of econometrics.
I believe that a multidisciplinary perspective is currently much required for development of behavioural economics and will soon be imminent. I have cultivated my skills with this belief I hope that they align with the requirements of your department. And the opportunities offered by your department will help me in expanding my knowledge and experience. I am sure that my enthusiasm, sincerity and the excellence of your program can help me explore behavioural game theory. I would be deeply honored to study at University College London. Thank you for your time and consideration.
| Post date | Users | Rates | Link to Content |
|---|---|---|---|
| 2024-06-07 | batterylow_123 | 58 | view |
| 2024-06-07 | batterylow_123 | 58 | view |
| 2024-05-01 | student193044 | 50 | view |
| 2024-04-13 | guozhishan | 66 | view |
| 2024-04-09 | guozhishan | 50 | view |
- Invest in unmanned space exploration. 69
- All results of publicly funded scientific studies should be made available to the general public free of charge. Scientific journals that charge a subscription or newsstand price are profiting unfairly. 50
- The Chevalier's memoirs. 81
- As people rely more and more on technology to solve problems, the ability of humans to think for themselves will surely deteriorate.Discuss the extent to which you agree or disagree with the statement and explain your reasoning for the position you take. 75
- Statement of Purpose 60
Grammar and spelling errors:
Line 1, column 104, Rule ID: CD_NN[1]
Message: Possible agreement error. The noun 'percentile' seems to be countable, so consider using: 'percentiles'.
Suggestion: percentiles
...our for securing a rank among the top 5 percentile in International Youth Math Challenge, ...
^^^^^^^^^^
Line 1, column 666, Rule ID: SENT_START_CONJUNCTIVE_LINKING_ADVERB_COMMA[1]
Message: Did you forget a comma after a conjunctive/linking adverb?
Suggestion: Thus,
...k 'Grammar Acquisition Game'. Thus my long term objective molded into rese...
^^^^
Line 5, column 682, Rule ID: SENT_START_CONJUNCTIVE_LINKING_ADVERB_COMMA[1]
Message: Did you forget a comma after a conjunctive/linking adverb?
Suggestion: Also,
... concepts which I find very intriguing. Also the workshops and seminars organised at...
^^^^
Line 9, column 447, Rule ID: KIND_OF_A[1]
Message: Don't include 'an' after a classification term. Use simply 'type of'.
Suggestion: type of
...narily stable strategy for learning the type of an opponent in a finitely repeated prisone...
^^^^^^^^^^
Line 9, column 612, Rule ID: AFFORD_VB[1]
Message: This verb is used with the infinitive: 'to model'
Suggestion: To model
... model and Temporal Difference Learning Model. I found that Temporal Difference Learn...
^^^^^
Line 9, column 661, Rule ID: AFFORD_VB[1]
Message: This verb is used with the infinitive: 'to model'
Suggestion: to model
...found that Temporal Difference Learning model was the evolutionarily stable strategy,...
^^^^^
Line 9, column 943, Rule ID: WHITESPACE_RULE
Message: Possible typo: you repeated a whitespace
Suggestion:
...on learnt through reinforcement learning and the proportion of population opting ...
^^
Line 13, column 406, Rule ID: COMPRISING_OF[1]
Message: Did you mean 'comprising' or 'consisting of'?
Suggestion: comprising; consisting of
...hat an individual can display behaviour comprising of different extremes rather than strictly...
^^^^^^^^^^^^^
Line 17, column 68, Rule ID: AFFORD_VBG[1]
Message: This verb is used with infinitive: 'to use'.
Suggestion: to use
...n Game' I modeled grammar learning using game theory. The Universal Grammar hypo...
^^^^^
Line 17, column 522, Rule ID: SENT_START_CONJUNCTIVE_LINKING_ADVERB_COMMA[1]
Message: Did you forget a comma after a conjunctive/linking adverb?
Suggestion: Thus,
...being taught than a dissimilar grammar. Thus the grammar being used in the environme...
^^^^
Line 17, column 574, Rule ID: THE_SUPERLATIVE[2]
Message: A determiner is probably missing here: 'have the greatest'.
Suggestion: have the greatest
...mmar being used in the environment must have greatest fitness, so a learner must select the e...
^^^^^^^^^^^^^
Line 17, column 835, Rule ID: THE_SUPERLATIVE[2]
Message: A determiner is probably missing here: 'with the highest'.
Suggestion: with the highest
...ite and the learner selects the grammar with highest fitness it will reach at the correct gr...
^^^^^^^^^^^^
Line 25, column 93, Rule ID: WHITESPACE_RULE
Message: Possible typo: you repeated a whitespace
Suggestion:
...rrently much required for development of behavioural economics and will soon be i...
^^
Line 25, column 144, Rule ID: ENGLISH_WORD_REPEAT_BEGINNING_RULE
Message: Three successive sentences begin with the same word. Reword the sentence or use a thesaurus to find a synonym.
...al economics and will soon be imminent. I have cultivated my skills with this bel...
^
Transition Words or Phrases used:
also, but, first, however, if, moreover, so, thus, while, as to, such as
Attributes: Values AverageValues Percentages(Values/AverageValues)% => Comments
Performance on Part of Speech:
To be verbs : 30.0 19.5258426966 154% => OK
Auxiliary verbs: 14.0 12.4196629213 113% => OK
Conjunction : 38.0 14.8657303371 256% => Less conjunction wanted
Relative clauses : 15.0 11.3162921348 133% => OK
Pronoun: 85.0 33.0505617978 257% => Less pronouns wanted
Preposition: 121.0 58.6224719101 206% => Less preposition wanted.
Nominalization: 51.0 12.9106741573 395% => Less nominalizations (nouns with a suffix like: tion ment ence ance) wanted.
Performance on vocabulary words:
No of characters: 5506.0 2235.4752809 246% => Less number of characters wanted.
No of words: 978.0 442.535393258 221% => Less content wanted.
Chars per words: 5.62985685072 5.05705443957 111% => OK
Fourth root words length: 5.5922259917 4.55969084622 123% => OK
Word Length SD: 3.47589312938 2.79657885939 124% => OK
Unique words: 464.0 215.323595506 215% => Less unique words wanted.
Unique words percentage: 0.474437627812 0.4932671777 96% => OK
syllable_count: 1760.4 704.065955056 250% => syllable counts are too long.
avg_syllables_per_word: 1.8 1.59117977528 113% => OK
A sentence (or a clause, phrase) starts by:
Pronoun: 23.0 6.24550561798 368% => Less pronouns wanted as sentence beginning.
Article: 10.0 4.99550561798 200% => Less articles wanted as sentence beginning.
Subordination: 2.0 3.10617977528 64% => OK
Conjunction: 4.0 1.77640449438 225% => Less conjunction wanted as sentence beginning.
Preposition: 9.0 4.38483146067 205% => Less preposition wanted as sentence beginnings.
Performance on sentences:
How many sentences: 45.0 20.2370786517 222% => Too many sentences.
Sentence length: 21.0 23.0359550562 91% => OK
Sentence length SD: 52.8427436414 60.3974514979 87% => OK
Chars per sentence: 122.355555556 118.986275619 103% => OK
Words per sentence: 21.7333333333 23.4991977007 92% => OK
Discourse Markers: 1.6 5.21951772744 31% => More transition words/phrases wanted.
Paragraphs: 7.0 4.97078651685 141% => Less paragraphs wanted.
Language errors: 14.0 7.80617977528 179% => OK
Sentences with positive sentiment : 27.0 10.2758426966 263% => Less positive sentences wanted.
Sentences with negative sentiment : 3.0 5.13820224719 58% => More negative sentences wanted.
Sentences with neutral sentiment: 15.0 4.83258426966 310% => Less facts, knowledge or examples wanted.
What are sentences with positive/Negative/neutral sentiment?
Coherence and Cohesion:
Essay topic to essay body coherence: 0.0 0.243740707755 0% => The similarity between the topic and the content is low.
Sentence topic coherence: 0.0 0.0831039109588 0% => Sentence topic similarity is low.
Sentence topic coherence SD: 0.0 0.0758088955206 0% => Sentences are similar to each other.
Paragraph topic coherence: 0.0 0.150359130593 0% => Maybe some paragraphs are off the topic.
Paragraph topic coherence SD: 0.0 0.0667264976115 0% => Paragraphs are similar to each other. Some content may get duplicated or it is not exactly right on the topic.
Essay readability:
automated_readability_index: 16.0 14.1392134831 113% => OK
flesch_reading_ease: 33.24 48.8420337079 68% => OK
smog_index: 11.2 7.92365168539 141% => OK
flesch_kincaid_grade: 13.8 12.1743820225 113% => OK
coleman_liau_index: 15.37 12.1639044944 126% => OK
dale_chall_readability_score: 9.3 8.38706741573 111% => OK
difficult_words: 286.0 100.480337079 285% => Less difficult words wanted.
linsear_write_formula: 15.5 11.8971910112 130% => OK
gunning_fog: 10.4 11.2143820225 93% => OK
text_standard: 16.0 11.7820224719 136% => OK
What are above readability scores?
---------------------
Write the essay in 30 minutes.
Maximum six paragraphs wanted.
It is not exactly right on the topic in the view of e-grader. Maybe there is a wrong essay topic.
Rates: 16.67 out of 100
Scores by essay e-grader: 1.0 Out of 6
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Note: the e-grader does NOT examine the meaning of words and ideas. VIP users will receive further evaluations by advanced module of e-grader and human graders.