• 必修科目至少 12 學分。
• 在學期間，每學期皆須選讀 0 學分的專題討論。
• 若課程中有（一）、（二）之分別，須依規定之先後次序修習。

 年級 科目代號 科目名稱 學分數 備註 上學期 下學期 一 L15021 機率論(一) 3 一 L15022 機率論(二) 3 一 L15061 數理統計(一) 3 一 L15062 數理統計(二) 3 一 L15031 分析通論(一) 3 一 L15032 分析通論(二) 3 一 L15041 代數通論(一) 3 一 L15042 代數通論(二) 3 一 L15071 數值分析(一) 3 一 L15072 數值分析(二) 3

 機率論、數理統計、分析通論、代數通論、數值分析
（資格考考古題可以在這裡找到）。各個科目資格考的參考書籍及範圍如下：
 科目 參考書籍及範圍 分析通論 1. Real Analysis (Royden) Part I (or Measure and Integral (by Weeden and Zygmund) ch.1-ch.8) 2. Principles of Mathematical Analysis (by Rudin) ch.7 and ch.11 Topics: (i) Lebesgue measure and Lebesgue integral (ii) Lebesgue's differentiation (iii) L^p-spaces (iv) sequences and series of functions 代數通論 Algebra (by Hungerford), ch.1-ch.6 機率論 1. A Course in Probability Theory (by Kai Lai Chung) 2. Probability Theory (by Yuan Shih Chow and Henry Teicher) (i) distribution funcation (ii) classes of sets, measure and probability spaces (iii) random variable, expectation, independence (iv) convergence concepts (v) law of large numbers, random series (vi) characteristic function (vii) conditional expectation, conditional independence, introduction to martingales 數理統計 1. Theory of Point Estimation (by Lehmenn) 2. Testing Statistical Hupotheses (by Lehmann) Topics: (i) group families, exponential families, sufficient statistics, completeness (ii) UMVU estimators, performance of the estimators, the information inequality (iii) location-scale families, the principle of equivariance (iv) Bayes estimation, minimax estimation, minimaxity and admissibility (v) convergence in probability and in law, large-sample comparisons of estimators, the median as an estimator of location, trimmed mean (vi) asymptotic efficiency, efficient likelihood estimations (vii) the Neyman-Pearson fundamental lemmas, distributions with monotones likelihood ratio (viii) unbiasedness for hypothesis testing, UMP unbiased test (ix) confidence sets, unbiased confidence sets, Bayes confidence sets (x) symmetry and invariance, maximal invariants, most powerful invariant test 數值分析 Numerical Analysis (by Burden and Faires) ch.1-ch.9