Abstract

Mathematics is the science and study of quality, structure, space, and change. It seeks out patterns, formulates new conjectures, and establishes the truth by rigorous deduction from appropriately chosen axioms and definitions. The study of mathematics makes a person better at solving problems. It gives someone skills that (s)he can use across other subjects and apply in many different job roles. In the modern world, builders use mathematics every day to do their work, since construction workers add, subtract, divide, multiply, and work with fractions. It is obvious that mathematics is a major contributor to many areas of study. For this reason, retrieving, ranking, and recommending Math answers, which is an application of Math information retrieval (IR), deserves attention and recognition, since a reliable recommender system helps users find the relevant answers to Math questions and benefits all Math learners whenever they need help solve a Math problem, regardless of the time and place. Such a recommender system can enhance the learning experience and enrich the knowledge in Math of its users. We have developed MaRec, a recommender system that retrieves and ranks Math answers based on their textual content and embedded formulas in answering a Math question. MaRec (i) applies KL-divergence to rank the textual content of a potential answer A with respect to the textual content of a Math question Q, and (ii) together with the representation of the Math formulas in Q and A as XML trees determines their subtree matching scores in ranking A as an answer to Q. The design of MaRec is simple, since it does not require the training and test process mandated by machine learning-based Math IR systems, which is tedious to set up and time consuming to train the models. Conducted empirical studies show that MaRec significantly outperforms (i) three existing state-of-the-art MathIR systems based on an offline evaluation, and (ii) a top-of-the-line machine learning system based on an online performance analysis.

Degree

MS

College and Department

Physical and Mathematical Sciences; Computer Science

Rights

https://lib.byu.edu/about/copyright/

Date Submitted

2023-05-30

Document Type

Thesis

Handle

http://hdl.lib.byu.edu/1877/etd12804

Keywords

Math IR system, formula search, tree matching, KL-divergence, recommender systems, TF-IDF, diversity

Language

english

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