Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2503.03960

Performance Comparison of Large Language Models on Advanced Calculus Problems

In Hak Moon
View original source ↗Read source document ↗Export metadata ↓

Abstract

This paper presents an in-depth analysis of the performance of seven different Large Language Models (LLMs) in solving a diverse set of math advanced calculus problems. The study aims to evaluate these models' accuracy, reliability, and problem-solving capabilities, including ChatGPT 4o, Gemini Advanced with 1.5 Pro, Copilot Pro, Claude 3.5 Sonnet, Meta AI, Mistral AI, and Perplexity. The assessment was conducted through a series of thirty-two test problems, encompassing a total of 320 points. The problems covered various topics, from vector calculations and geometric interpretations to integral evaluations and optimization tasks. The results highlight significant trends and patterns in the models' performance, revealing both their strengths and weaknesses - for instance, models like ChatGPT 4o and Mistral AI demonstrated consistent accuracy across various problem types, indicating their robustness and reliability in mathematical problem-solving, while models such as Gemini Advanced with 1.5 Pro and Meta AI exhibited specific weaknesses, particularly in complex problems involving integrals and optimization, suggesting areas for targeted improvements. The study also underscores the importance of re-prompting in achieving accurate solutions, as seen in several instances where models initially provided incorrect answers but corrected them upon re-prompting. Overall, this research provides valuable insights into the current capabilities and limitations of LLMs in the domain of math calculus, with the detailed analysis of each model's performance on specific problems offering a comprehensive understanding of their strengths and areas for improvement, contributing to the ongoing development and refinement of LLM technology. The findings are particularly relevant for educators, researchers, and developers seeking to leverage LLMs for educational and practical applications in mathematics.

Explore related subjects

cs.CL

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

In Hak Moon. 2025-03-05. Performance Comparison of Large Language Models on Advanced Calculus Problems. https://arxiv.org/abs/2503.03960

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

What is the Role of Small Models in the LLM Era: A Survey

Large Language Models (LLMs) have demonstrated remarkable capabilities in various reasoning tasks, which leads to the development of increasingly large models. However, scaling up model sizes results in significantly higher computational costs and energy consumption, which makes these models impractical for academic researchers and businesses with limited resources. At the same time, Small Models (SMs) are frequently used in practical settings, although their significance is currently underestimated. This raises important questions about the role of small models in the era of LLMs, a topic that has received limited attention in prior surveys. In this work, we systematically examine the relationship between LLMs and SMs from two key perspectives: Collaboration and Competition (or Complementarity). We hope this survey provides valuable insights for practitioners, fostering a deeper understanding of the contribution of small models and promoting more efficient use of computational resources.

cs.CL↗
arXiv2026

SG-FSM: A Self-Guiding Zero-Shot Prompting Paradigm for Multi-Hop Question Answering Based on Finite State Machine

Large Language Models with chain-of-thought prompting, such as OpenAI-o1, have shown impressive capabilities in natural language inference tasks. However, Multi-hop Question Answering (MHQA) remains challenging for many existing models due to issues like hallucination, error propagation, and limited context length. To address these challenges and enhance LLMs' performance on MHQA, we propose the Self-Guiding prompting Finite State Machine (SG-FSM), designed to strengthen multi-hop reasoning abilities. Unlike traditional chain-of-thought methods, SG-FSM tackles MHQA by iteratively breaking down complex questions into sub-questions, correcting itself to improve accuracy. It processes one sub-question at a time, dynamically deciding the next step based on the current context and results, functioning much like an automaton. Experiments across various benchmarks demonstrate the effectiveness of our approach, outperforming strong baselines on challenging datasets such as Musique. SG-FSM reduces hallucination, enabling recovery of the correct final answer despite intermediate errors. It also improves adherence to specified output formats, simplifying evaluation significantly.

cs.CL↗
arXiv2026

A Course Intelligence Platform for Higher Education: Lessons from AI-Assisted Course Evaluation

The rapid adoption of generative AI has created new opportunities for teaching, learning, and quality assurance. Existing applications, however, remain largely student-facing, with comparatively limited attention to institution-level needs. This paper presents a course intelligence platform deployed across more than 100 universities and serving over 10,000 instructors in China. By linking competency requirements, knowledge structures, teaching activities, and assessment evidence, it establishes a shared foundation for knowledge organization, instructional design, learning assessment, and quality evaluation. The course evaluation module is examined as a representative institution-facing application of the platform, which integrates national evaluation standards, structured educational evidence, customized prompting strategies, and domain-adapted LLMs to generate quantitative scores and qualitative feedback. A case study involving 100 authentic university courses is conducted to evaluate its alignment with expert judgments and the interpretability of its outputs. Statistical analyses show substantial agreement between AI-generated assessments and expert ratings, while qualitative results highlight the credibility of the feedback. The findings further suggest that AI-assisted evaluation requires not only capable models but also structured domain knowledge and transparent criteria. In this context, human ratings should be treated as an informative reference rather than an error-free gold standard, and the objective is to achieve consistent, interpretable, and defensible judgments instead of merely replicating expert scores.

cs.CL↗