Title: CUMath: A Benchmark and Evaluation Framework for LLMs on Mathematical Reasoning in Undergraduate Computational Math
Primary area: datasets and benchmarks
Keywords: Large Language Models, Symbolic Reasoning, Mathematical Reasoning, Evaluation Framework, Evaluation Metrics, Error Analysis, Reasoning Failures

Abstract: Large Language Models (LLMs) perform well on popular math benchmarks but still struggle with fundamental undergraduate tasks such as basic integrals. This suggests a diagnostic gap: existing datasets are either trivial, synthetic, or overly advanced, limiting their usefulness for exposing reasoning failures. To address this, we introduce CUMath, a benchmark of 2,100 real problems from undergraduate courses in Calculus, Linear Algebra, Differential Equations, and related fields. Each problem includes step-by-step solutions, enabling evaluation of both final answers and intermediate reasoning. Moreover, current evaluations treat accuracy and reasoning separately, overlooking their joint role in problem-solving. To address this, we propose a multi-layered evaluation framework that combines automatic metrics with an LLM-as-a-grader pipeline, integrating symbolic encoding and external verification. Using this setup, we evaluate 15 LLMs across various prompting strategies. Our results show that even advanced models often misuse symbolic methods and rely on shortcuts, leading to polished but flawed solutions. Our findings reveal the ongoing issue of inconsistent reasoning, highlighting the need for improved benchmarks, evaluation frameworks, and the development of models with enhanced consistency and reasoning capabilities. The code and data will be available upon publication.