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Title PageversoTable of ContentsPREFACE1. SET NOTATIONObjectsSetsSubsetsRule of specificationExerciseComplementsIntersectionUnionExerciseOrdered pairs and Cartesian productExerciseOne-to-one correspondenceMappingsExercise

2. MATHEMATICAL INDUCTIONA proof by inductionThe well-ordering principleThe principle of mathematical inductionExerciseMiscellaneous remarksAnother version of the principle of mathematical inductionExerciseRecursive formulaeExercise

3. COMBINATORICSBoxes and ballsExerciseRemarksPermutationsExercisePermutations in which repetitions are allowedExercisePermutations of objects some of which are alikeCircular permutationsExerciseCombinationsExerciseCombinations with repetitionsExerciseBinomial theoremExercise

4. ARITHMETICAbsolute valueExerciseDivisibilityEuclidean algorithmExerciseThe greatest common divisorExerciseThe least common multipleAn effective division algorithm for the evaluation of gcdExercisePrime numbersThe fundamental theorem of arithmeticThe infinity of prime numbersExerciseCongruenceChinese remainder theoremExercise

5. REAL NUMBERSThe number lineExerciseSome basic assumptionsExerciseSome well-known inequalitiesExerciseDenseness of the rational numbersPostulate of continuityExercisePowers and rootsExistence of rootsPowers and logarithmExercise

6. LIMIT AND CONVERGENCENull sequenceExerciseConvergent sequenceDivergent sequenceExerciseSum, product and quotient of convergent sequencesThe sandwich theoremExerciseMonotone sequenceCauchys convergence testExerciseSeriesGeometric series and harmonic seriesSome useful rulesTest of convergenceExerciseAppendix

7. COMPLEX NUMBERSEquations and number systemsOne-dimensional number systemTwo-dimensional number systemComplex numbersStandard notationsExerciseComplex conjugateEquations with real coefficientsExerciseDe Moivres theoremExerciseThe n-th rootsExerciseGeometry of complex numbersCirclesStraight linesExerciseAppendix

ANSWERS TO EXERCISESINDEX