Noumena asked about books on the modern mathematical reinterpretation of Marx's economics, in addition to Morishima, and Robert Vienneau was spot on with his mention of Sraffa and Roemer. Let me attempt a more systematic answer.
Marx's economic theories are a critique of, and also a continuation of, the classic tradition of political economy in which the two great names before Marx are Smith and Ricardo. It was Marx's great misfortune that in the decade after he published volume one of CAPITAL, a theoretical revolution took place in mainstream economic theory, usually referred to as the marginalist revolution, led by three theorists working simultaneously and independently of one another: Jevons, Menger, and Walras. The result was to change fundamentally the nature of the questions asked by economists, and to sweep into the dustbin of history not only Marx but also Mill, Ricardo, Smith, and the rest of the classical school. Marx's disciples continued to write and talk as he had done, making them look, over the years, more and more quirky, cranky, sectarian, and, dare I say it, marginal. Eventually, Paul Samuelson could get away with describing Marx as a "minor post-Ricardian autodidact." [I have always thought that for Samuelson, the author of the most successful college economics text ever written, the autodidact part was what particularly ticked him off.]
This was pretty much the state of play until 1960, when Piero Sraffa, an Italian economist living and working in Cambridge, England, published a little book not quite one hundred pages long, called PRODUCTION OF COMMODITIES BY MEANS OF COMMODITIES. Sraffa was the editor of the magisterial multi-volume edition of the works of David Ricardo, and his work might easily be viewed as a resurrection and justification of Ricardian theory, but lest one have any doubt about where Sraffa's sympathies lay, we should recall that it was he who brought the paper, ink, and pen to Antonio Gramsci with which Gramsci wrote his PRISON NOTEBOOKS. Although Sraffa makes use only of the most elementary mathematical operations, and writes in a spare, monastic style, his work really builds on the linear programming work of Wassily Leontieff.
In the thirty years or so after Sraffa's little book appeared, an extraordinary world-wide theoretical discussion arose among well-trained theoretical economists who were sympathetic to the classical and Marxian programme, and were disenchanted with the General Equilibrium models then all the rage. This was no small mathematical quibble. What was at issue was nothing less than what economics ought to be talking about. The classical school asked two great questions: How does the annual social product get divided up among the three classes in society [landowners, entrepreneurs, workers]? And, What are the conditions for stable continuous economic growth? These questions focused attention on class conflict and class division, which Smith and Ricardo, as well as Marx, thought was central to capitalism. They also focused on issues of growth versus stagnation. The neo-classical school asked totally different questions: What is the rational way to allocate scarce resources with alternative uses? How does subjective desire or preference determine market price? It was, of course, possible for them to ask about distribution and growth, but since those questions did not lie at the heart of their theories, their answers were ad hoc and rather unsatisfactory ["each factor in production is paid its marginal product" etc.]
Marx said many things in his economic writings, of course, but central to them were a series of theoretical claims, about the relationship between exploitation and profits, about the inner contradictions of a capitalist economy, about the falling rate of profit, and so forth. Following Sraffa, the new mathematical Marxists, as I may call them, undertook to translate Marx's theoretical claims into modern dress, using essentially linear algebra rather than differential calculus. This involved making a different set of simplifying assumptions than those underlying neo-classical theory. [So, for example, in the neo-classical marginalist models, it is assumed that there is a contunuously infinite number of alternative production techniques combining inputs in varying quantities. The mathemtatical Marxists make the opposite simplfying assumption that at any one time, there is a single dominant production technique, that can be represented by a vector of quantities of inputs per unit output. The mathematical result is that instead of twice differentiating a continuous production function, you invert a matrix of input coefficiants.]
Speaking very broadly and generally [and revealing my own prejudices], these theoreticians demonstrated that Marx had a full-blown mathematically quite respectable theory that was in fact correct about a good many things, wrong about some others [the falling rate of profit had to go -- thanks to a theorem by Okishio, later re-proved more simply by Bowles]. I myself made a small contribution to this literature [in a paper, online now, I believe, called "A Critique and Reinterpretation of Marx's Labor Theory of Value"], although John Roemer, bless him, noted that a year before I published. a very similar result had been proved by an Spanish economist writing in Spanish. [sigh. This never happens in philosophy.]
So, here is a short list of some of the best books in this large and excciting literature. I have actually read all of these, believe it or not. It cost me a good deal of effort, but was well worth it.
Morishima, MARX'S ECONOMICS, 1973
Luigi Pasinetti, GROWTH AND INCOME DISTRIBUTION, 1974
Andras Brody, PROPORTIONS, PRICES AND PLANNING 1974
Abraham-Frois and Berrebi, THEORY OF VALUE, PRICES AND ACCUMULATION 1976
Luigi Pasinetti, LECTURES ON THE THEORY OF PRODUCTION 1977
Ian Steedman, MARX AFTER SRAFFA, 1977
Walsh and Gram, CLASSICAL AND NEOCLASSICAL THEORIES OF GENERAL EQUILIBRIUM
Luigi Pasinetti, STRUCTURAL CHANGE AND ECONOMIC GROWTH 1981
John Roemer, ANALYTICAL FOUNDATIONS OF MARXIAN ECONOMIC THEORY 1981
Stephen Marglin, GROWTH, DISTRIBUTION, AND PRICES 1984
If anyone is interested, I can say a bit about what each of these has to offer, but sufficient unto the day.
