Calculemus -- The Rooster and the Butterflies -- Optimising Problem Formulation for Cylindrical Algebraic Decomposition -- The Formalization of Syntax-Based Mathematical Algorithms Using Quotation and Evaluation -- Certification of Bounds of Non-linear Functions: The Templates Method -- Verifying a Plaftorm for Digital Imaging: A Multi-tool Strategy -- A Universal Machine for Biform Theory Graphs -- MKM -- Mathematical Practice, Crowdsourcing, and Social Machines -- Automated Reasoning Service for HOL Light -- Understanding Branch Cuts of Expressions -- Formal Mathematics on Display: A Wiki for Flyspeck -- Determining Points on Handwritten Mathematical Symbols -- Capturing Hiproofs in HOL Light -- A Qualitative Comparison of the Suitability of Four Theorem Provers for Basic Auction Theory -- Students' Comparison of Their Trigonometric Answers with the Answers of a Computer Algebra System -- DML -- Mathematics and the World Wide Web -- Structural Similarity Search for Mathematics Retrieval -- Towards Machine-Actionable Modules of a Digital Mathematics Library: The Example of DML-CZ -- A Hybrid Approach for Semantic Enrichment of MathML Mathematical Expressions -- Three Years of DLMF: Web, Math and Search -- Escaping the Trap of Too Precise Topic Queries -- Using MathML to Represent Units of Measurement for Improved Ontology Alignment -- Systems and Projects -- A Web Interface for Isabelle: The Next Generation -- The ForMaRE Project - Formal Mathematical Reasoning in Economics -- LATExml 2012 - A Year of LATExml -- The MMT API: A Generic MKM System -- Math-Net.Ru as a Digital Archive of the Russian Mathematical Knowledge from the XIX Century to Today -- A Dynamic Symbolic Geometry Environment Based on the GröbnerCover Algorithm for the Computation of Geometric Loci and Envelopes -- ML4PG in Computer Algebra Verification -- Pervasive Parallelism in Highly-Trustable Interactive Theorem Proving Systems -- The Web Geometry Laboratory Project -- swMATH - A New Information Service forMathematical Software -- Software for Evaluating Relevance of Steps in Algebraic Transformations -- The DeLiVerMATH Project: Text Analysis in Mathematics.

This book constitutes the joint refereed proceedings of the 20th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, Calculemus 2013, 6th International Workshop on Digital Mathematics Libraries, DML 2013, Systems and Projects, held in Bath, UK as part of  CICM 2013, the Conferences on Intelligent Computer Mathematics. The 7 revised full papers out of 18 submissions for MKM 2013, 5 revised full papers out of 12 submissions for Calculemus 2013,  6 revised full papers out of 8 submissions for DML 2013, and 12 revised full papers out of 16 submissions for Systems and Project track presented together with 3 invited talks were carefully reviewed and selected, resulting in 33 papers from a total of 73 submissions.